I got a pair of headphones that my dog chewed through the wires. I'd like to repair them by soldering the wires. However, when I stripped off the insulation, I find the wires have an additional insulation of paint or laquer. If I try to scrap this off with say a knife, I either cut through or break off strands, and/or I only get a bit scrapped of the outside. Same thing trying to sand the coating off. I tried some acetone in attempt to dissolve it without any luck.
Is there some technique to getting this coating off or am I just SOL here?