Is your phone unlocked? If so...
This is your SIM card. Take it out.
When you are in the Caribbean, buy a prepaid sim card (cell phone stores, airport, convenience stores?) and put it in. Give people you want to have the number the number.
The other option is to keep your current plan, but screen your calls. Only pick up calls from numbers and people that you know. Turn off all 3GS functions, you don't want to use a roaming data plan for internet unless it's absolutely neccessary.