I'm one of those who talks about the bait chum starting to look good.
You can certainly buy canned sodas from the bar (or your mini-bar, if you have one) and take those ashore, no problem. If there is a restriction on an island, it's fruits and vegetables. But I can't say that I remember any such restrictions on a Western Carib cruise. And I know I've done it. Don't forget zip-top bags for ice and to hold your goodies.
As to the water shoes, I only know from Captain Marvin, but plenty of people were wearing them. My husband and I were among them.
Hint: If you are very fair-skinned use a high SPF lotion and wear a nasty old T-shirt when you are in the water.