yes, this is very fixable and frankly, just has to be done sooner or later.
That is the classic stator break in wiring. I had to do mine last weekend.
Go to a boating supply place if there's one nearby and buy yourself about 8 feet of marine grade tinned wiring. 18 gauge is fine. I got 16 and it was much thicker than what I was trying to replace.
That sheathing is fine to remove, it's standard rubber wiring beneath. The fiberglass around it is to keep it from moving due to vibration. Trim it back and expose enough rubber wire so that you can solder it and not end up with the joint in that rubber tunnel when you're done. if you solder the wires end to end, don't do it in a straight line. Do it at like a 45 degree angle because the wire has to bend up towards the rubber tunnel piece and then slide thru. Overly tinning the wire before soldering and then trying to bend it later to fit inside will be a pain. If you don't over heat/ over tin before you solder the wire will be more flexible. Remember it has to deflect out of the way of the rotor by the time you're done.