Just be sure to take a trip to Sting Ray City in Grand Cayman, either with a ship excursion or on your own, but its worth the time, one of the best tours in the Western Caribbean. Have heard a lot of cruisers that have been very happy with booking this through Capt. Marvin:
Are there any other things you are thinking about seeing/doing? There are some more private tour companies that may be what you are looking for. What ship are you cruising on?