(you still call it the Army Air Force, I believe?)

Not since end of The Late Great Misunderstanding when Air Force was established as a separate branch of the Armed Forces.
It is now : United States Air Force (USAF)

In WWII Army Air Force Officers sometimes went overseas aboard troop ships.

The only time I know for sure that the Army Air Force flew off US warship was from the "Hornet" which was the "base" for the famous raid on Japan led by General Jimmy Doolittle.

As for shoes, navy officers, in peacetime, used to wear white shoes with the white uniforms used in warm climes and as they came down ladders the shoes were a tip off to crew that an officer was descending on them (and the illegal craps game!)
wow