The NOAA has some month-by-month hurricane incidence maps on their website. They're only meant to be qualitative, but they can give you a sense of what you're up against:
From this we see:
The ABC islands, along with Trinidad & Tobago, are less commonly affected by hurricanes than most of the rest of the Caribbean. All of these islands are relatively close to the South American mainland, and so take a little longer to get to from the continental US; but the extra travel time might be worth it in this case.
Cuba is relatively less-frequently hit than other Caribbean islands (perhaps due to the sheltering effects of nearby Hispaniola?) US citizens will have trouble traveling here, of course.
If you want to avoid hurricanes, Puerto Rico and the Leeward Islands are not the best choices during the months of August and September. The Bahamas, Jamaica, and Hispaniola are better, but probably not much.
Finally, note that hurricane tracks can go pretty much anywhere in the Caribbean (warning: huge image file); just because you decide to go to Aruba doesn't mean you won't be affected by a hurricane. I would probably buy travel insurance for peace of mind in a case like this, but YMMV.
