The requirement to produce ID and CHP on demand in NC is NOT dependent on whether or not you have a CHP.
The ID/CHP requirement is ENTIRELY predicated on carrying concealed under § 14‑415.11.(a). If you are CCing, and are asked for ID and CHP, you have to produce it.
OC is not mentioned, and therefore it is NOT regulated under this statute, and the requirement to inform and produce ID upon request is NOT APPLICABLE.
Any activity which is not prohibited is legal and lawful.
An LEO demanding to see your CHP when you are OCing is NOT a "lawful order" because no permit is required to OC under NC law, and NC is NOT a "stop and identify" state. Unless you are operating a motor vehicle, there is NO requirement that you produce (or even possess) a DL or other photo ID in NC...
So, basically, if an LEO sees you OCing and asks to see your ID and CHP, you are not required to say anything to him other than to indicate that if you are being detained, you wish the presence of your attorney before you can answer any questions (if you want to play hardball).
If you want to play nice, you could give your name and address verbally.
But there is NO requirement whatsoever to produce ANY sort of paperwork if you are OCing and not operating a motor vehicle in NC. Any LEO who would arrest you for failing to produce a DL or CHP for OCing is a Federal Civil Rights lawsuit waiting to happen, IMO, and I will GLADLY facilitate their entry into the Federal Courts if they insist on behaving in such an unlawful manner...
But then again, IANAL, and my opinion is worth exactly as much as you paid for it...