I've been away for 2 weeks and not sure where you are with this motor or even if you intend to try a rewind but you may find it easier to salvage the wire from the microwave oven fan motor if the wire size matches, I've found that the fan motor windings are usually not dipped in varnish which make it easy to get to the wire. The transformer is usually welded together which means taking a side grinder to it to get to the windings which are often - but not always - dipped in varnish.

Not sure what you have in your junk box but another good source of wire is old 3 phase contactor sets, the 24v coil ones will usually have wire that will be too thick but the 240v coils usually have wire around .12mm in diam.