You won't have much trouble taking dollars. In all my travels there was only one port where they didn't take them in the Caribbean, can't atm remember which, but right on the pier was a teller window right outside where you can exchange. I just wanted a coke after an excursion and skipped it due to the line. Also every ship I've been on exchanges currency for the guests, though how much of each kind is limited of course.
I would ask the concerige on day 1 if you need to change from Euro/dollar over and if at all needed they will say which ports dollar might not be adviseable. Most ports are safe-ish but I'd reccomend taking $50 and leaving the rest in your room safe.
Just take $US for small things & use a credit card (with care) for anything larger. Do be careful about exchange rates as the various islands have different currencies, some use the $EC, some like Barbados have their own national currency $BDS, all these have different exchange rates against the dollar & it has been known for unscrupulous persons to quote in local but then insist it was $US which is several times more money.
This is a great little site but is mostly American based.
Some answer questions...I also question answers