Think twice please
Dear Water,
Bob makes some very good points-this is not an ideal boat for this trip.
Remember also that if you decide to go through the Islands (as opposed to the offshore route), you will be sailing UPWIND the entire time. In the Winter months, you will see ESE winds of 18-25 knots (and seas of about 6-8 feet) as the norm-hardly fun sailing upwind in a 23' boat. In the summer, the breezes will be somewhat lighter, but less predictable. And these are the good conditions! When the daily thunderstorm comes through with 30-45 knots of wind in the squalls, the "fun meter" heads south in a hurry.
Your other option, which is also not great for a boat this small, is to do the offshore route, whereby you reach out (close or beam reaching) on an Easterly heading for about 800 miles-DEEP into the open Atlantic-until you pick up the Prevailing NE trades, tack, and beam reach down to the islands.
This is likely a 14 -18 day passage to somewhere like Tortola or thereabouts for a boat like this. It will be much faster that the Island hop, but you won't have to beat the whole time. You will, however, be sailing in the same 20-30 knots of wind, 6-12 foot seas (typically-although they can be much taller), and VERY, VERY far from land. Can't say I recommend this either.
If you are hell bent on sailing the boat there, take about 3 months (at least) during the summer, and PICK your days, make 1-2 day legs, and stop frequently for weather. You could easily spend a week or more waiting for your day to sail, but at least you will be in a nice place.
Trying to go straight through either way will be very roughy duty for the boat, not to mention to poor crew. Possible? Yes. Suggestion? Put it on a freighter and ship it. I can almost gurantee it will be cheaper and faster, not to mention safer..Why cheaper? You will be spending a lot of time and money doing repairs, eating in restaraunts, hotels (the boat will be unliveable after some of these legs), etc.
Sorry to burst your bubble, but this is a very rough trip-I have done it both ways-numerous times, and on all kinds of boats (smallest was about 30 feet, largest 84 feet).
Safe sailing!
S