Originally Posted by Nos4r2
NOTE-If you do this make sure you silicone up the end of the heatshrink to stop water getting in, and make sure the wires are in the positions you want them while you heat it. They'll go stiff after heatshrinking. and moving them isn't a good idea if you can help it.
Or use the adhesive lined heatshrink. This'll help hold the bits of the crumbling insulation together AND will give you a waterproof repair. Just make sure that you get the right size shrink so that the glue inside the h/shrink bonds all the way round the surface of old wire.
As Matt suggests, it should work a treat!