Without some local assistance, it could be a mistake to try entering from the east into Walker's. Don't think I'd try it. The prevailing wind from the east could present a "rage" condition as you arrive.
As far as the Gulf Stream goes, it varies in speed considerably. This has to be figured on a current basis (no pun). It's not always running at 4 knots and only runs max right in the center (which also needs to be checked as to position). On Passage Weather today, for instance, current adjacent to Ft. Pierce is running quite slow:http://www.passageweather.com/maps/f.../rtofs/024.png
so if setting out the actual current needs to be figured and not some rule of thumb about how fast the Stream runs.