When looking for knife laws, your best bet is your state's General Assembly site. All current laws are public on the web.
In the case of NC, the law you are looking for is this one,
§ 14‑269. Carrying concealed weapons:
http://www.ncleg.net/EnactedLegislation/Statutes/HTML/BySection/Chapter_14/GS_14-269.html
To sum it up in plain English, the law prohibits carrying "any bowie knife, dirk, dagger,... razor, shurikin, ...or other deadly weapon of like kind"
concealed. There is are no provisions prohibiting the open carry of any of these items. So you can open carry a fixed blade if you want. When carrying concealed, it has been my experience in reading case law for years that when a law contains the terms "bowie knife," and "dirk" but does not define them, they can easily be construed by an arresting officer to encompass
any fixed blade knife. Often an arrest or citation will be made, with the idea that the judge will sort out whether or not the concealed fixed blade is considered an illegal concealed weapon. Evidence of intent and the circumstances that lead to a cop going through your pockets in the first place seem to play a far larger role that the design of the knife itself.
This law does have several exceptions. These include being on your own property, being a cop, being military specifically ordered to carry the weapon, or if the "weapon" is a folding knife of any size that is not a switchblade or balisong. If being prosecuted under this law, you are allowed a logical defense:
It is a defense to a prosecution under this section that:
(1) The weapon was not a firearm;
(2) The defendant was engaged in, or on the way to or from, an activity in which he legitimately used the weapon;
(3) The defendant possessed the weapon for that legitimate use; and
(4) The defendant did not use or attempt to use the weapon for an illegal purpose.
Lastly, "concealed" is not defined in this statute. But generally speaking this is the best model to follow:
If I am not a cop and can both see the knife while talking to you, and can identify immediately that it is a knife and not some other object, it is not concealed.