The fans +/- wires are covered by a thin protective sleeve.

Apply some electrical or kaptom tape to patch it if necessary.

Initially I tried to use shrink tubing here but the smallest diameter I could get around the plug was a 3/8" tube which will not properly seal around the cable when heated

If you accidentally cut through the entire cable (+/- wires) you'll have to resolder them together and cover with shrink tubing.