No silly questions if you need to know!
The main thing to remember is that the airlines will not allow spray cans in carry-ons, but you can pack them in your luggage (I believe - someone correct me if I am wrong, its been a long time since I used spray cans for anything - my sunscreen comes in tubes).
But even with tubes the airlnes limit you to 2.5 ounces per tube. So you need to put it in your carry on luggage. The cruise lines don't care how much you bring on.
And YES - the Caribbean sun will burn you very quickly - before you even realize it, so put on that sunscreen before you go outside.