Marshall Islands

Wallis's Voyage

The Dolphin came across Rongalep and Bikini on 03/09/1767. Wallis identified them as the Piscadone Islands.

The Dolphin is shown on one stamp from 1999. There was an American schooner in the 19th century called the Dolphin, and this has also been featured on a stamp issued by the Marshall Islands in 1992.

Cook's ship, the Resolution, has been featured on two sets.

Marshall Islands	26/08/1999	Early European Explorers 4x1v The Dolphin in 1767 under the command of Samuel Wallis is shown on one of these four 33c stamps.
Marshall Islands	14/02/2004	225th Anniversary of Captain Cook’s Last Voyage 3x1v HMS Resolution is shown on two of these se-tenant stamps - once in rough water and once sailing through ice. USS Bonhomme Richard is shown on the third stamp.
Marshall Islands	02/04/2008	Sailing Ships 12x1v HMS Resolution is shown on one of these 41c stamps.

Northern Mariana Islands

Byron's Voyage

After an unproductive visit to one of the Gilbert Islands, the Dolphin and Tamar headed due north through the Marshall Islands without sighting land, before heading for Tinian. They found it along with the neighbouring islands of Saypan and Aiguigan on 30/07/1765. They found the island less accommodating than they had hoped with poor water supplies, mosquitoes and incessant heat. Two of the crew died of fever whilst there. They were the first to have died on the expedition, and a further three of the Tamar's crew were drowned when going to the north of the island to hunt cattle.

Wallis's Voyage

Wallis and the Dolphin visited Tinian for repairs and refreshment in September and October 1767.

The Northern Mariana Islands are a Commonwealth in free association with the United States, whose stamps they use.

Palau

Carteret's Voyage

The Swallow appears to have sighted a number of the outer islands of Palau. Unfortunately the details in the journal are rather scanty, and it is difficult to be sure. The main island of Palau was first put on the map by the American ship the Antelope in 1783.

There aren't any stamps related to our navigators.

Pilipinas

Byron's Voyage

After leaving the Northern Mariana Islands, the Dolphin and Tamar sailed through the Bashee Strait between Taiwan and the Philippines, where they sighted several of the islands but did not stop. They then sailed south, at some distance from the west coast of the Philippines, and on through the Spratly Islands.

Wallis's Voyage

Wallis took the Dolphin through the Bashee Strait sighting Grafton Island on 28/10/1767.

Carteret's Voyage

Carteret and the Swallow reached the island of Mindanoa on 01/11/1767, where they stopped briefly before heading for the Macassar Strait and then on to Batavia.

I don't believe any of these explorers have yet been shown on any Philippines stamps.