I been on a few cruises and this is my experience

Excursions are good, if it is something really unique, that you cannot find admission to it, other than by booking through the cruise.

My family and I booked every excursion on our first cruise in the Caribbean, after that we only did for one or so, there are always taxis at the pier looking for tourists, and chances are they will take you to the same places as the cruise line, cheaper, and you decide how long to take at each place, something might attract you more than the rest of the cruise organized excursion.

So, if it's for island sightseeing do it on your own, depends on the length of the cruise, but if you want do it solo on the first port, if you don't feel that you are comfortable doing it that way, make reservations with the cruise, they always have plenty of space, but make sure you ask

Have a wonderful time and don't forget the Dramamine