My parents live on the other end of the island from where you will be and I've spent a good deal of time there. As far as I know there are no knife shops in that area. There is a gun shop in Morehead City which isn't too far away and they may carry a few knives. There are various fishing tackle and sporting good stores as well but most won't stock anything unusual.
There is a nautical store in Beaufort called "Scuttlebutt" that carries a few knives but as i recall they are mostly Sypderco stuff.
The only thing I can think of is you might consider taking a jaunt over to Jacksonville. Since its a military town it's three major industries are topless joints, used car dealerships and pawn shops. You might find something nice if you search those pawn shops and actually Jacksonville might have a knife shop of some kind as well. Thats the closest place I can think of that might have anything. You'll most likely be going through Goldsboro as well and it may be worth your time to do a yellow pages check for a knife shop there as well.
Oh, and there is an Army/Navy Store in Havelock that carries knives. You might try there.
One last place, but I wouldn't hold out much hope for quality here, there is a Flea Mall on Highway 70 in Morehead City that is open on weekends. There are usually knife dealers set up there.
Now for the important stuff...where are you going to eat?
Some suggestions: If closer to Wilmington you might try Pearl's for seafood. My cousin's husband owns it and its really good. You've got to love a place that has a plate called "The Barge".
In Emerald Isle or there abouts...try The Crab Shack and if you make it down the beach a ways to Beaufort, Clawson's on the waterfront is really good.