the way they used to do it without an engine was head
north for the trades,
sail out to bermuda
reach down into the carribean,
then ride the current
around and back up to the keys.
i assume you don't want to spend a year at sea though.
done the trip down the coast a lot.
hang in tight inside the stream is good advice, but if it gets nasty
and you have no engine you're going to have to ride it out.
Big trouble comes when you hit hawke channel.
Stay outside and you are in the stream which is a no go headed west.
Stay inside and it can get tricky if the wind
doesn't fill in and give you
good steerage in those confined quarters.
Pick your season carefully. In the summer you get becalmed with lots of
thunderstorms in that channel and you'll find yourself on a reef or aground in short order.
I wouldn't do it without an engine or without a longer route
giving me some sea room.
but yeah, its possible.