i burned mine, and its cut off about 4 inches up.

I cut one off a car at the parts yard, but the wire consists of 1 multithread covered wire, and that is wrapped with wire, then another plastic coating goes around that.

Can I just peel the outer layer off both sides, and take that wire wrapped around, and twist it together, and solder/heat shrink tube it, and then do the same to the inner wire? Or should I use butt connectors?

I need to get this thing replaced, but dont wanna fuck anything up, and from what I remember people saying in the past, these wires are not good to mess with. Just wanna do it right. Any suggestions?