How can I eliminate a light circuit?
You should check the voltage of the light, many times under cabinet lights are low-voltage (eg, 12V) and run by a transformer. If there's only one, I doubt someone would have gone through the effort, but it's possible.

You can't just close wires off inside the wall. You must terminate them properly in a junction box, and that box must be accessible. This means if you don't want the wires to power anything, you need to at least have a blank faceplate. 

The junction box needs to be securely mounted, the wire needs to be connected into the box properly (how this is done depends on the box used), and it must be grounded, and the wires capped with wire nuts. If you are considering doing this job yourself, I highly recommend you make sure you 100% understood everything I just said, and also go buy a non-contact voltage detector.

If you hire an electrician to come in, no, you don't need to worry about inspectors - the electrician will do that, if required. Mostly, around here anyways, the inspectors only come and inspect something like 1 in 10 installs done by electricians they know (selected basically at random). Only if they find faults, will they start coming more often, and the reputation of the electrician/company will go down. Likely after a couple problems, the electrician is out of a job. It's in the electricians best interests to always do the job properly.