In 1790, 17-year-old Shaw and his brother left Ireland for the fledgling United States, arriving in New York City before heading to the nation's capitol of Philadelphia.

[1] In late 1797, Shaw was the sailing master of a brig that traveled to the West Indies and returned to the States in spring 1798, having been harassed by French Naval ships in the lead-up to the Quasi-War.

[1] Shaw was appointed a lieutenant on 3 August 1798, and his first assignment was USS Montezuma, patrolling the West Indies from November 1798 through October 1799 under Alexander Murray.

[5] The schooner Victory was laden with "valuable cargo from Norfolk", and had been sailing under the French flag for five days when Shaw recaptured the ship for the United States.

[1] Shaw's one-year tenure as Enterprise's skipper made the schooner "one of the famous vessels of the Navy";[5] the two together captured more French privateers than any other American ship in the West Indies.

[1] Taking command of USS George Washington on 4 May 1801, Shaw sailed the vessel to deliver tribute to Algiers, and repatriated Americans who had been captured by the deys there.

In February 1807 at Natchez, Mississippi, Shaw mustered 61 guns, 448 US Military men, and the ketches Ætna and Vesuvius to capture the former vice president of the United States (VP).

"[5] This assignment placed Captain Shaw under Major General James Wilkinson, the commander of all United States Armed Forces in the Louisiana Purchase since 1803.

Wilkinson had been part of the Burr conspiracy before betraying the former VP, and though repeatedly acquitted, Shaw disliked serving under the man; his protestations to the Navy Department earned him naught but an order to cooperate with the senior Army officer.

"[5] When the War of 1812 broke out with the United Kingdom of Great Britain and Ireland, of the 14 gunboats vital to the defense of New Orleans, Shaw only had ten operational.

[8] While combat eschewed the Gulf until the war's waning years, and Shaw worked to prepare coastal defenses (including a blockship),[1] he also had to contend with "extensive" piracy and smuggling on his coast.

Excepting his 20 March – 20 September suspension by court-martial for "unofficer like conduct", Shaw remained in Greater Boston until requesting transfer to a warmer climate on 26 May 1823.