I would suggest just getting a cheap pair of keds type sneakers for them to wear (they usually run about $5 at Walmart). They will be alot better on the feet if you are cave tubing in Belize then aqua socks.
But also being from Wisconsin I would say you aren't going to have much luck other then the expensive name brand aqua socks.
Are you going to Miami a day early? There was a Walgreens near the hotel we stayed at that carried aqua socks, about $9/pair, and the guy we were traveling with picked a pair up. They carry them year round in Florida, you can even find them at grocery stores there.