[Reece]

Sure, Litz wire would be fine, better than what was there. Modern Litz you just solder, the hot solder melts away the invidual enamel on the strands. However, if you can salvage the original wire and make it look good, that's what I'd do. You can take one end loose and try to tighten the whole thing up as a unit, then reattach the wire. If that doesn't work, you'd have to unwind it and to keep it from kinking, you can unwind it loosely into a cardboard box on the floor, then rewind from the box by hand. Have some strips of duct tape at hand to anchor it temporarily if you have to stop in between. Old timers used to shellac finished coils. You could also use spray lacquer.