What happens if I shave a little sliver off electrical wire with a utility knife?
If you are talking about something the size of a splinter then you have no problem. I doubt if you shaved enough off to change the ampacity of the wire.  The main reason not to use a knife (other than safety) is scoring the electrical wire and making it easier to break off.  Wire strippers normally go enough of the insulation to make it weak enough to come off with little effort.