DJM...I don't think there IS an offshore ROUTE from Georgetown since you are too far south to sail and have many miles into the teeth of the trades heading west before you can turn south. Unless you have VERY large fuel capacity you will probably find yourself heading northeast rather than southeast until you hit approximately 60 west when you can turn through the wind and head south to the VI's.
I do know people in large boats with excellent fuel supplies that have done the westing under motor out of New Providence channel but they complained about days of bashing into the seas and wind and being so relieved when they could finally turn.
One piece of advice if you DO decide to go this route is to get underway as a cold front passes through the Bahamas so you can ride it aways before having to crank the motor on or bear off to the north. Of course fewer fronts make it to the Exumas so perhaps it may be better to stage for the trip in Nassau or the Abacos.
If it is any consolation...the thorny path is no fun either!