Bhutan

This landlocked Asian country issued one stamp in 1989 showing Cook. That might seem daft in itself but the whole set was devoted to the International Maritime Organisation's 30th Anniversary. During 2000, Bhutan released a 100nu miniature sheet of Captain Cook as part of a Discovery and Navigation issue. The other miniature sheet in this set featured Christopher Columbus.

Bhutan	24/08/1989	30th Anniversary of the International Maritime Organisation 12v & 12xM/S(1v) This set shows a total of 24 different ships. Resolution in the icebergs in 1772 is shown on one of the twelve 25nu miniature sheets.
Bhutan	18/09/2000	Discovery and Navigation 2xM/S(1v) Captain Cook is featured on one of these two 100nu miniature sheets.

Royaume du Cambodge

Cambodia issued a set in 1982 featuring Navigators and Sailors. Captain Cook and the Endeavour were shown on the 15r stamp.

Etat du Cambodge

01/08/1992

Navigators and Sailors 5v Captain Cook and the Endeavour are shown on the 15r stamp in this set.

Republic of China

Cook's Third Voyage

The Resolution and Discovery passed the island of Formosa during the return journey after Cook's death.

I don't believe the Republic of China (Taiwan) has ever produced any stamps connected with these explorers.

People's Republic of China

Cook's Third Voyage

The Resolution and Discovery sighted the Lema islands on the approach to Canton during the return journey after Cook's death.

I don't believe the People's Republic of China has ever produced any stamps connected with these explorers.

Republik Indonesia

Byron's Voyage

The Dolphin sighted the coast of Sumatra on 15/11/1765 and then passed through the channel between Sumatra and Bangka Island, and heading for Batavia on neighbouring Java. They stayed at Batavia for several weeks repairing the ship, taking in supplies and contracting deadly fevers. They then sailed through the Sunda Strait and on to the Cape of Good Hope.

Wallis's Voyage

Wallis called in at Batavia in need of amongst other things a replacement anchor, which he was unable to purchase at a reasonable price. This visit to Batavia, like most resulted in most of the ship's crew going down with fluxes.

Carteret's Voyage

The Swallow reached the Strait of Macassar (14/11/1767), sailed to Macassar on Sulawesi (15/12/1767), and then on to Bonthain. When they first arrived at Macassar, the Dutch Governor told them to leave immediately. The crew were dying daily from scurvy and because of the desperate situation, Carteret told the Governor that if they were not given assistance, they would run the ship aground. The Swallow was then allowed to sail a short way down the coast and moor in Bonthain Bay. They stayed there for five months, recuperating, repairing the ship and waiting for the winds to take them to Batavia. The Swallow sailed from Bonthain Bay on 22/05/1768, having received the news that the Dolphin had been in Batavia.

The Swallow reached Batavia on 03/06/1768. During the next three and a half months, the Swallow was careened and repaired as best they could, but it was of the opinion of the Dutch carpenters that she would not make it to the Cape of Good Hope. Whilst at Batavia and Onrust, where the repairs were carried out, Carteret behaved in a rather haughty manner towards the local council and the Governor. For example, he would refuse to stop his carriage in deference to the Governor's or those of the Councillors. He also refused to attend a celebration of the marriage of the Prince of Orange on the grounds that he would be sat at a table of lower station than the Councillors. The Swallow did manage to recruit some English sailors, which helped replace those lost during the voyage. They set sail on 15/09/1768, anchoring in the Strait of Sunda on 20/09/1768, finally leaving on the 25/09/1768.

Cook's First Voyage

The Endeavour reached Batavia towards the end of the first voyage. Cook lost thirty of his crew to fever caught at the port, which was a shame as he had managed to prevent scurvy from taking anyone during the whole voyage.

Cook's Third Voyage

The Resolution and Discovery stopped for a short while at Princes Island before heading for the Cape of Good Hope. This was during the return journey after Cook's death.

I don't believe Indonesia has ever produced any stamps connected with these explorers.

Democratic Peoples Republic of Korea

In 1980 the DPR issued a set devoted to Conquerors of the Sea, which included a 70ch stamp featuring Cook, a ship and navigational instruments. The stamp was also featured singly in a miniature sheet. In 1988, at least one miniature sheet was issued to commemorate Australia's Bicentennial showing Cook's ships.

DPR Korea	30/04/1980	Conquerors of the Sea Five 70ch stamps in a miniature sheet. One features Cook, a ship, map and navigational instruments. The stamp is also featured singly in a miniature sheet which also features the crew on a ship.
DPR Korea	30/07/1988	Australian Bicentennial 80ch miniature sheet featuring the Pembroke at Whitby and Cook on the border. According to SG, it shows the Resolution. There might be more than one m/s.

Laos

Laos issued a set of Navigators and Explorers in 1983 that included a 5k stamp featuring Cook and the Resolution.

Postes Lao

08/10/1983

Navigators and Explorers Captain Cook and the Resolution are shown on the 5k stamp in this set.

Macau - China

Cook's Third Voyage

The Resolution and Discovery anchored at Macau during the return journey after Cook's death.

I don't believe Macau has ever produced any stamps connected with these explorers.

Malaysia

Byron's Voyage

The Dolphin stopped at Timoan Island off the East Coast of Malaya for a couple of days in November 1765, but found it impossible to buy any supplies from the locals.

Wallis's Voyage

The Dolphin passed the islands off the east coast of mainland Malaysia in November 1767, but did not stop. I'm not aware of Malaysia producing any stamps related to the explorers.

Maldives

Our explorers always sailed well to the South when going through the Indian Ocean and so never got close to the Maldive Islands.

The Republic celebrated Cook's Birth Anniversary and Discovery of Hawaii in 1978. In early 2000, the Maldives released a sheetlet of stamps showing events of the second half of the 18th Century including Cook.

Republic of Maldives	15/07/1978	250th Birth Anniversary of Captain Cook and Bicentenary of Discovery of Hawaii 7v & M/S(1v) The Dance portrait is shown on the 1l stamp. The 2l stamp shows the statue of Kamehameha I of Hawaii. The 3l value shows HMS Endeavour. The 25l stamp shows the route of the third voyage. The 75l stamp shows the Resolution and Discovery and a map of the Hawaiian Islands. The 1r50 stamp shows Cook meeting Hawaiian islanders in ship. The 10l stamp shows the death of Cook. The 5r miniature sheet shows the Endeavour differently to the 3l stamp. Both the stamps and M/S were also released in an imperforate limited edition.
Maldives	01/02/2000	Millennium 1750-1800 17x1v Captain Cook is given pride of place in this sheetlet of seventeen 3Rf stamps and one label. His double sized stamp shows the Dance portrait and a painting of the Endeavour. He is also given a mention in the text on the border of the sheetlet. This was part of an IGPC omnibus.

Mongolia

Mongolia issued a set of 8 stamps back in 1981 showing famous ships. The Resolution is shown on the 80m value.

Mongolia

01/08/1981

Famous Ships 8v The Resolution is shown on the 80m stamp in this set of eight.

Nippon

Cook's Third Voyage

The Resolution and Discovery passed the islands of Japan and encountered Japanese ships but did not land. This was during the return journey after Cook's death.

I don't believe Japan has ever produced any stamps connected with these explorers.

Spratly Islands

Wallis's Voyage

The Dolphin sighted several of the islands in this group over a couple of days, giving them titles such as Sandy Island and New Island. Viêt Nam, Malaysia, Philippines and China all lay claim these islands.

Timor Leste

Cook's First Voyage

After repairing the Endeavour in Australia and then sailing through the Torres Straits, Cook passed the island of Timor before stopping at Savu island.

I'm not sure where Occussi Ambeno is. I think it was a tiny Portuguese enclave in western Timor. When these stamps were produced, East Timor had been invaded and occupied by Indonesia, and so they are best regarded as propaganda labels.

Occussi Ambeno

//1979

Cook Overprints on Birds 7x1v, 1v & 2xM/S(1v) Cook's portrait is overprinted on each of the seven 40c, one 80c, and the $2.00 and $3.00 miniature sheets, which otherwise show birds.

United Arab Emirates

Before the UAE was established, the various sheikhdoms each issued stamps. Umm al Qiwain issued a set sometime in 1972 which featured Cook on one of its values. The set is mentioned in the appendix in the main catalogues, as it probably never saw use in the post.

Umm al Qiwain

//1972

Famous Sailors 8v Cook and the Endeavour are shown on the 15d value in this strip of 8 setenant stamps.

Viêt Nam

Wallis's Voyage

Wallis passed the island of Condone (Con Soon or Con Doa) after making his way through the Spratly Islands.

Cook's Third Voyage

The Resolution and Discovery passed Con Doa during the return journey after Cook's death.

I'm not aware of any stamps produced by Viêt Nam related to any of these voyages.