When I go to any beaches, I just wear some sandals, I'm sure any athletic shoe would also be fine, what ever the kids are comfortable wearing would be fine. If they already have water shoes, those too would be good, but I wouldn't go out and buy them just for going to the beach.
A definite pack item, I found the "ugly" black strap type sandals that resemble tires in my opinion work well too. Just make sure there is a back strap as flip flops come off.
I would go with the idea of the shoes perhaps making a one way trip--so much sand, and sometimes smell. Yes, there is definite coral and items to step on.
Don't forget boys dandals can fit girls and women for a cheaper price.
San Juan: Dorado beach: Embassy Suites Hotel beach: Gorgeous pool, extremely rocky and coral "man made cove area, not what I'd call a quality beach.
St. Thomas: Saphire beach--very nice, offered shade, some areas coral or rough ocean floor.
Antigua: Line? beach (across island from dock) nice sand, literally dropped off 50 feet from beach. No need for shoes.
St.Maarten: Orient beach---shoes needed for walk to beach, Atlantic side-waves etc, and optional clothing. Not the prettiest of the beaches we were at. We stayed at family end but some people still wandered "naked"
you will need some type of footwear to get to the beach, walk on the hot sand and you will also need some type of footwear on the ships decks. We love the Teva type water sandals ( LL Bean, Land's End are the same, much cheaper), flip flops work ok, as do canvas tennis sneakers. The beaches of St. Thomas are like silk.