I'd recommend you still check with your local travel vaccination centre for the inoculation you might need.
In our case it was recommended we get Hep A and a Tetanus/Diphtheria shot. As the cruise ship is not in port for more than a day you normally need not worry but as soon as you venture into tropical areas or local food and water, it is good to be prepared
Hepatitis A - Wikipedia, the free encyclopedia
Some of the Islands per the World Health Centre still have Dengue fever due to stagnant water with mosquito's so you can obtain and put on a good tropical lotion when walking in shorts and short sleeve shirts much like sun screen.
Take at least sun screen of 30+ and wear a hat when walking for a few hours as the Caribbean sun is very different and enjoyable.
Both are good for several years
Anyhow, your call , just offering some advice to consider