Please understand that I am not an electrician, and my repair technique is simply "hammer and tongs" style. What you are trying to do here is reestablish the connection of the copper portion of the wire. No need to replace any parts. A good set of electrician's wire strippers and tape is all you need.
First, unplug the switch at the box. Then, cut the wire and get rid of any weak or damaged pieces. Carefully separate each end of the wire to a length of four or five inches, so you have essentially two wires from each end. You will need to strip about one-half inch of the rubber jacket from the ends of each of the four pieces of wire. The one difficulty with this repair is that the diameter of the copper wire is so small, it is easy to cut into the wire. Just make sure you have enough copper wire showing so as to maintain an appropriate contact when you twist them together. I simply wrapped each wire in tape with the best quality electrician's tape I could find, then wrapped the whole thing in tape again. Voila...hammer and tongs repair.
By the way, you may want to dump some bleach in the pool if your SWG is off too long. I hope this answers your question.