On a well found boat your voyage should take 8 or 9 days staying east of the Bahamas until you reach the North East, North West Providence channel, then zip through that directly to Ft Lauderdale or points north. If you are heading for Miami or the Keys you would use the Old Bahama channel. Virtually nowhere along either route is there a good hurricane anchorage, so it would not be prudent to consider being near any of the islands you are passing for that reason.
At that time of the year, I would make it a "mad dash" trip and forget about sightseeing.
I've done that trip a number of times delivering sailboats. The best way to go is between the Bahamas and Cuba through the Old Bahama Channel. You will be sailing west/northwest, which means you will have an almost dead, down wind sail. There tends to be traffic in the channel, so you will want to be sure you have experienced crew who know what to look for. Also, it seems every time I go through there, I get boarded by the Coast Guard. They don't make you stop. They radio first and then approach with an inflatable for the "at speed" boarding. Last time I got boarded they gave us some bread and a newspaper before leaving. Not bad!
Once out of the Old Bahama Channel, if you are going up the east coast, get in the Gulf Stream for a sled ride to your destination. If you are going up the west coast, stop in Key West for a breather and then head on to your home port a day or so away.
Here's a picture of the Coasties and me the last time I went through the channel.
If you do the Bahama Chanal be sure you have charts of no. coast of Cuba in case you need to find a hurricane hole. Not the best time of year to do that trip and not many places to run away from a storm except Luperon, DR.
The approach to the Old Bahama Channel goes just north of Puerto Rico and the Dominican Republic, both of which provide a place to duck in out of weather. At the east end of the channel is Great Inagua and Matthews Town with a fairly good harbor. I've been in there, and it can provide a place to sit out bad weather; although I would be concerned about tidal surge in a strong storm. The harbor is very small with a narrow opening to the west.
Once you leave Great Inagua behind, it is approximately 360 NM to the Cay Sal Banks and another 150 NM to the Florida Keys. I have looked at charts for the north Cuban coast in the past and I'm not sure I would want to try to go there in bad weather.
Going up the east side of the Bahamas puts you in open water for several days also. You aren't going to escape that. If you are overly concerned about your exposure to bad weather, the time frame you are planning for the delivery is probably not the best.
As billyruffn notes, Luperon is really your only good hidey hole, I'm make sure you were confident of the weather before getting too far past there. Next best spot to probably run and hide would be New Providence or Grand Bahama.
I'd plan on giving the Turks & Caicos a miss, unless you don't mind getting hit up for a very expensive fee for even the shortest of visits...
If you do go via the Old Bahama Channel, make sure you have a very solid crew whom you can trust on your off watch... That can be a tiring run, a long narrow gauntlet with a lot of shipping traffic, bordered by a largely unmarked reef to the north... Depending on where your destination is in FL, and all other things being equal with a decent forecast, I'd favor capta's route, passing N of the Silver Bank and T&Cs, and passing thru the Bahamas via the Providence Channels, or perhaps into Exuma Sound. If your destination is S Florida, a decent route can be to pass thru the Exumas around Staniel Cay, and take the Decca Channel into the Tongue of the Ocean, up thru NW Channel, then across the bank to South Riding Rocks, which can give you a decent angle for crossing the Stream to S Florida...
If for no other reason, I'd favor passing thru the Bahamas simply because it affords you the opportunity to take a break, if the crew is feeling the need. That option really doesn't exist on the Old Bahama Channel route, unless you're gonna enter Cuba, or perhaps make a stop on the Cay Sal Bank... And, it goes without saying, AIS would be really nice to have for the Old Bahama Channel. On a boat without it, I'd be much more inclined to go up thru the Bahamas, instead...
Good luck, keep a sharp eye on the weather in the NW Caribbean, that's the most likely spawning ground for a tropical system that time, as TS Andrea developed in early June of last year...