The house we are renting soon has its own boat dock on the sound.....

While I would love to say we have a big fishing rig, we do not.

Are there any places in Hatteras that rent fishing skiffs at a reasonable price?

Hatteras Parasail looks like they rent boats from Oden's Docks. I've never used them so I can't vouch for them. We rented from an outfit in Rodanthe last summer and the guy we dealt with was a bit of a jerk, so I wouldn't recommend them.

Unfortunately not down your way but Fishing Unlimited next to the "Little Bridge" on the Manteo Causeway rents both Pontoons and a limited amount of small skiffs. There is a huge Liability Insurance concern with renting boats. Not here but up North many places stopped because they couldn't afford the Insurance along with constant motor maintenance

We rented a skiff from Hatteras parasail one year, but only for a half day. I see they do have weekly rates, if that is your intent. They gave us a brief tutorial, sort of like a test-drive, even tho we are accomplished river boaters (have 2 boats of our own, as well as canoes, kayaks.) I assume the tutorial was routine, and perhaps required by insurance. And they tell/show you where you can and cannot go. The sound is a different animal than any river. Anyway, very nice, knowledgeable ppl. Set us out on our own, and we had a great time, fishing and just boating.