OK, this is one of those rare posts in which I’m going to just state that this is a repair that you probably shouldn’t do if you don’t know what you’re doing because if you frak it up you could start a fire or even kill yourself.
But if you are comfortable with electricity and do have some idea of what you’re doing this is a relatively straightforward fix.
A few years ago I purchased a nice Shark Navigator vacuum. At the time we had two dogs. Well, puppies actually, and the same day that I bought the vacuum one of the puppies chewed through the power cord when I stepped away for just a moment. Fortunately it wasn’t plugged in at the time. Unfortunately I could not find a replacement cord and so my only option was to cut out the section from where it connected to the vacuum up to just past the break where the puppy had chewed it. The connection point can be accessed by removing some screws and a plastic plate from the bottom of the cannister along with some additional screws; make sure to reconnect the stripped wire sections properly in there.
Finally, after a few years I was able to find a full-length replacement cord and thus I’m no longer forced to frequently unplug and replug the cord into different locations. The cord for my Shark Navigator model is the HQRP AC Power Cord for Shark Navigator Lift-Away Pro NV355 NV356 NV356K NV357 NV355CS NV356KCS NV356E Upright Vacuum + HQRP Coaster, which cost $17.95 (and an additional $9.95 shipping charge).
Updated 04/18/2018: I haven’t had any problems with the replacement cord. It’s worked great since it was installed.