I have read several accounts of WW2 warships, and in the tropics it wasnt uncommon to rig a salt water pool on deck for the sailors to cool on in.
There was that tank of saltwater one doused oneself in at the end of shellback initiation, but that’s another topic entirely.
Way back when, navy swimwear was UDT shorts, which had to be worn with skivies underneath for obvious reasons. Back when military booty shorts were a thing in the US navy, the French Foreign Legion and the Rhodesians.
I was stationed on the Lexington probably about the time you visited. And yes, we had the b-ball goals in the hanger bay along with several weight rooms scattered throughout the ship. Also, the hanger bay deck had a sort of “running track” outlined on the outer edges with distances marked. When traversing the bay during normal operations, you were expected to defer to the runners.
“Steel Beach Picnic” on the Lex. They had some “homemade” (really the machine shop made them) grills made out of 55 gallon drums cut in half that they’d bring up with a bunch of chips and sides from the galley along with a bunch of canned soda, sweet tea, and bug juice in big dispensers, etc. The officers were expected to grill burgers and dogs for the crew. The CO always made sure to be seen cooking. The XO, the Air Boss, and ChEng were always there as well. Obviously, more junior officers did the bulk of the work. 
My father uses the same quote about his time in the Navy during Viet Nam. That is all he ever said about his service.
My dad was in Underwater Demolition in WWII so swim trunks were part of his uniform. Scroll down a bit for a pic.