No one on here is aware of your medical history and unqualified to give medical advice. It is unlikely you will need anything serious but for peace of mind contact your GP and the practice nurse will go through it with you based on your itinery. They have access to the latest up to date information. Although there is nothing complusory there may be some advisory ones like hepatitis.
No vacs needed. Very easy to DIY if you only go to this site that I direct every one to - Try google and 'cruise ports call boards' - the first result will give you all the info under the section for each island
We have never had vaccinations when visiting the Caribbean islands you mention. Our practice said no need.
Ask the pharmist at your local Boots. They are always very uptodate delighted to help and free. No I do not work or have any conection with boots. But have found there advice to be better than my GP's.
We have visited the Carribben several times in the last few years and we have never had vaccinations, if you are at all worried about anything it is best that you speak to your practice nurse and she will be able to advise you on what you have to do, she will most likely give you a leaflet that explains everything. I am not a qualified nurse but I do have some knowledge of how the medical profession works. BUT DO SEEK THE PROPER ADVICE FOR YOUR OWN SATISFACTION. Hope this is of some help for you.
Not a doctor but have visited the caribbean many times(cruising and not) and all I have needed is a tetanus booster. Phone your local surgery and ask their proffesional advice, it's free and it will put your mind at ease.