That should be fun. The first 20nm up the lee side of Grenada will be motoring (wouldn't recommend going windward as it will be a beat and the swell can be pretty big, not great for your first sail) then it usually gets breezy and fun for the rest of the trip to Union. If you do get short of time you can always anchor up at Carriacou and clear out. Next day, early start and up to Blue Lagoon, St Vincent to clear in (if you had to stop at Carriacou rather than Union). It won't necessarily be a beat, it depends on time of year. I've done that and had a beam reach on more than one occasion.

Pick up the rest of the crew and make the rest of the trip leisurely so that everyone wants to do it again.