I sincerely believe this would be a dangerous trip for a number of reasons. And, I agree with Dave, stay inside at least until you reach Morehead City, NC. It's a nasty stretch of water, the inlets are among the most dangerous on the East Coast and that tiny outboard motor would never be able to handle the standing waves let along the incredibly strong currents.
Once you arrive in south Florida, that MSD and outside showers is going to be a problem. Most of south Florida is a No Discharge Zone. All sinks, galley and head, must be routed to a holding tank. Yes, you can take an outdoor shower, but the soapy water cannot be discharged overboard. There was a thread pertaining to this on the Sail Net not too long ago, but I'm not sure where it is. You could also Google the Florida Marine Patrol site and get the necessary information about discharging overboard.
As Dave said, "Safety First".