It really depends on your sailing skills & what you are sailing.
My girlfriend & I have a great time romping between islands of the Eastern Caribbean
in 20 to 35 knots of wind
& 4 to 8 foot seas. But we reef the boat for the conditions & keep her sailing 6 to 9 knots, not dogging out & crashing into the waves. We've a 53' heavy displacement ketch
No one else can tell you how to sail your boat; you either have the experience & knowledge or you should get that experience first, close to home.
As mentioned above, there is not going to be a safe "weather window" at this time of year. You might get lucky, or you might get VERY unlucky & lose your boat and/or your lives if you try for the Caymans from Florida
this time of year without the experience necessary to survive a hurricane
A word of warning; rocks sink vessels. You are much safer at sea than trying to seek shelter in an anchorage you are unfamiliar with (at least on a well found boat) if you do have a hurricane bearing down on you.
Even without a hurricane, the summer thunderstorms in the Caribbean
can be a bit breezy. If you cannot see under one (day or night you can
see them coming) take everything down & just wait it out. I've had something like 70 knots in the leading edge of thunderstorms, after the calm preceding it.