When you find this out, let all of us know. Currently my crystal ball is in the shop and won't be fixed for a few more months. Last year was a much different year for a lot of islands than the norm - what will this year bring ?????
So... might not get much help in the " Caribbean " forum. Its not well viewed and most members only monitor specific island forums they frequent and are familiar with.
As a " general " rule, the father south you go the less likely of rain / hurricanes. Would not suggest Bermuda as its usually in the main path. Barbados is a bit hit or miss ( usually more miss ) however they get enough tail end winds / tropical storms that could last a few days.
Aruba is your best bet although not a cheap island to visit. Typically Aruba get about 3 - 5 " of rain a year since its a desert but last year they did see some major flooding due to well above average rainfall ( after August though ). IMO also not much culture but the amazing beaches can be quite busy will wall to wall people depending on location. Are you going all inclusive or condo / villa type rental ?
For perhaps more choices, try Google and see what other island have typically less amounts of rainfall ( even by month )