Okay, here's the root of the problem. Everywhere that the superglue touched, and subsequently the acetone and rubbing alcohol caused the insulation to harden and in some places crystalize. If there is no short, electrical tape will provide a short term solution -- the glue on the tape will eventually fail and become a sticky mess. A better solution is to open the headphone and pull the worn insulation into the housing. Once the casing is opened you should find a couple of small tabs that the wire can be wrapped around or tied around to prevent it from moving back and forth in the housing. Quite frequently the factory ill have tied a knot in the wire just inside the housing. You would be replicating this same knot a little further down on the wire.
If there is a short in the wiring, then the only way to repair it is to shorten it PAST the exposed portion -- typically the short will be in the exposed area, and shortening the wire to that point will only cause you to have to make the same repair twice -- and resolder the wires to the drivers.
Hope this helps