there'll only be the one wire, the other nubs on the case end are likely rivets holding something in that end, maybe the bushing plate and/or a cardboard insulator .... to replace the wire you have to loosen the 2 screws visible there which go all the way to the other end, probably threaded into the gear head, although you should open that first to see if there's nuts on that end, because the shaft will be hooked to something
the larger part of the case will probably want to come off the rotor, in which case the brushes [on that end] will pop loose, and they're not particularly easy to get back in place - can be disassembled with care, but yes, some of the small DC motors are a struggle to open because everything is tightly interwoven and sometimes the bearing on the spindle end is really tight
if you can slip some insulation on the wire as suggested it'll save deleting a few expletives and grinding yer teeth to nubs

also there's "liquid electrical tape" that applied into the hole should do fine to prevent it shorting to the case
Bill