While I haven't traveled to the islands in September since 1998, when I found myself stuck on Tortola to ride out Hurricane Georges, my "normal" Caribbean travel schedule now includes a trip down island in November, which is still hurricane season, though not the peak.
I have had to cancel my November trips twice due to hurricanes. Both times, the trips were insured. Between generous cancellation policies during storms and trip insurance, I was not out any money. Not being out any money also helped me avoid the disappointment of not taking a trip during the scheduled week, because for me and my husband, actually getting the time cleared on the calendar is as big a consideration as anything else. With the funds free, I've been able to book a last minute trip somewhere else. Both times, it was Bahamian hurricanes that spoiled the trip, so we re-booked the day before departure to the BVI once and to Nevis another time (using FF miles, even, as seats become available at the last minute).
That said, Grenada is a pretty safe hurricane season destination, though a hurricane elsewhere might mess up your travel, depending on where you are transiting through. Trip insurance is helpful to cover those delays or interruptions.