The Naval Historical Center has several images including the Naugatuck, including these (and others):
In April, the ship was apparently under the command of a Captain Shippen. By May 8 (the action against Sewell's Batteries) and through at least May 15 (the action at Drewry's Bluff), US Revenue Service Lt. David C. Constable was in command.
Unfortunately, I have not yet collected the names of the other crew. Any help would be appreciated.
[T1] Message of the President of the United States to the Two Houses of Congress at the Commencement of the Third Session of the Thirty-Seventh Congress, Vol. 3. 1862. House of Representatives, 37th Congress, 3rd session. Ex. Doc. 1. Washington, DC. 1862. 931pp