I assume you re talking about Morehead City/Beaufort NC. We draw 5 ft and came thru there last spring. There were a few shallow spots north of Coinjock, but you should be OK if you are careful and do this part at high tide.
The Dismal Swamp canal is still closed to all traffic, but it is not deep enough for you anyway.
We prefer the Pamlico Sound route rather than the Alligator River. Manteo is probably too shallow, but you will have no problem getting into Ocracoke.
The best marina on the whole ICW is River Dunes, just north of Oriental.