You need to get some adhesive lined heatshrink, in a few diameters, Large one is placed over the cable before you start fixing it, and then you peel back insulation, and use smaller ones to seal the individual wires after you solder then together. small diameter, shrink on each, then a large adhesive lined one over the join, shrink down , and then a second one, longer than the first, to seal. Hellerman Tyton has some good quality ones, you want them to have an unshrunk diameter a little larger than the cables to be used on, and then you need to extend beyond the damage by around 10cm with the outer sleeve.