We're from eastern NC and visit that area several times each year. There are three oceanside commercial campgrounds (all in the Avon/Rodanthe area) that I'd recommend - Ocean Waves, Camp Hatteras and KOA. Ocean Waves is the least expensive (I did not say cheap), Camp Hatteras the most costly. If you just want somewhere to sleep, there are several other private options but, if the missus is gonna be hanging around the camper a lot, I wouldn't suggest them.
You might consider Frisco Woods which is five miles or so south of the Hatteras Light
- its on the sound side but has full hookup water front sites and, if you're looking for places to kayak, this is a better base for that in my opinion.
Personally, any of the four Federal campgrounds are better than the private offerings but, as you've noted, no hookups available. I doubt you'll need the AC in late April - maybe use an inverter for the TV?
If you have any specific questions I'll be happy to give em my best shot.