According to North Carolina Firearms Laws published by the state Attorney General's office:
"An "antique firearm" is one that was
manufactured on or before 1898 and includes any firearm with a matchlock, flintlock,
percussion cap, or similar ignition system, or a replica thereof if the replica is not designed
or redesigned for using rimfire or conventional centerfire fixed ammunition. It also includes
any muzzle loading rifle, muzzle loading shotgun, or muzzle loading pistol, which is
designed to use black powder substitute, and which cannot use fixed ammunition. N.C.
Gen. Stat. § 14-409(a) The term “antique firearm” shall not include any weapon which
incorporates a firearm frame or receiver; is converted into a muzzle loading weapon; or is
a muzzle loading weapon that can be readily converted to fire fixed ammunition by
replacing the barrel, bolt, breechlock, or any combination thereof. A "historic-edged
weapon" is defined to be a bayonet, trench knife, sword, or dagger manufactured during or
prior to World War II, but no later than January 1, 1946. N.C. Gen. Stat. § 14-409.12"
This quote appears in the section "North Carolina Requirements" which states that antique firearms, as defined, are exemnpt from the transfer permit requirement.
I could find no reference to antique firearms regarding carrying. It does say that minors are prohibited from carrying handguns as described in NCGS 14-269.7 which is to say
"A firearm that has a short stock and is designed to be fired by the use of a single hand, or any combination of parts from which such a firearm can be assembled."
This definition technically includes antique pistols.
A minor may carry one for instructional purposes in the presence of a supervising adult and while hunting outsidean incorporated city limit with the written permission of a parent or legal guardian.
To be safe, you should probably carry only under those two conditions.