I have never been there, so I can't say for certain. My first thought was that it's just another part of NC, so OC should be good to go except in the usual free kill zones. Then I remembered that a lot of that area is designated as wildlife refuge and parks so I pulled up google maps and, sure enough, a lot of the outer banks are colored green. And that is where the line gets a little blurred for me. If it is a national park, then you're good to go (except for the federal buildings). If it is a state park, then you're not so good to go - you'll have to conceal. I'm not sure about national wildlife refuges, reserves, and the like.
If you dislike the term, then simply use the actual words: The Outer Banks. Letters and words are free - use them!... was wondering how friendly OBX (Hate that term!) is to open carry.