You are correct in the fact that you need A/C. The reason I ask is because I put an aftermarket A/C in my car and it works great. I did have an existing system, but I can't say it made it any easier.
I used a VintageAir Compac II system, which was not really made for C-3 Corvettes, but I understand they now make a system for our cars. You can contact the person I used here in Texas (Lewis Makeovers 281-485-7366) in Pearland, TX. and he can let you know who else might be able to assist you in NC.
When I put mine in over a year ago, Roger Lewis was the only person selling VintageAir products that put them in C-3 Corvettes and his knowledge led them to consider selling a system that better fit our cars.
I like it because it takes up less space in the engine compartment, total removal of the air box on the firewall, smaller compressor, uses 134a refrigerant and a smaller, more effecient condenser coil.
It's worth considering. I like it in mine and we get into the high 90's and low 100's in the summer.