Unfortunately its all too easy to damage good quality modern test leads - silicone insulation may be heat resistant but it is a lot softer and rips more easily than the old-fashioned PVC, and the probes and plugs are almost invariably moulded on so aren't rewirable.
I must emphasise that Zero999 is right: Damaged leads *SHOULD* be cut up immediately in a workplace, makerspace, or formal educational environment, but if one tells an impoverished maker hobbyist who's never going to go over the 30V from their bench PSU that, they'll probably laugh at you and ignore all your other advice. If you do decide to risk keeping damaged test leads, *PLEASE* tag them 'Damaged: 50V MAX' and keep them in a locked draw to stop numpties killing them self with them!
I have bad memories of replacing plugs on VGA cables, in the days when monitors had wired in cables . . . . It was always preferable to find a 'near enough' replacement cable from a scrap monitor and fiddle with the pin order of the PCB end till it matched, and transplant the cord grip rather than having to solder the center row of a DE-15 plug, then get everything to fit in a metal DE back shell!