Hi Hillary, and welcome to the forums. There is a lot of experience out there with our members and many of them are willing to share their knowledge to help us all.
I agree with Sterling that you should replace all wiring that looks suspicious. You say that you will be cleaning and recapping the set, so that would be the time to replace the bad wires as well. When you are replacing the capacitors and out-of-tolerance resistors, just jiggle the wiring and you will easily tell if it needs replacement. The insulation is probably rubber (not plastic) and if it’s bad it will crumble when you grip it in your pliers. (It’s interesting that some colors of this old insulation seem to stand up better than others. Some colors crumble, others turn soft and mushy.) Dont be too worried about getting the lead dress exactly perfect when you replace the old wires – just put the new ones as close to where the old ones were as you can. You have taken good pictures to help you here.
Keep us in the loop as you go along and post some pictures when you’re done!