With a normal soldering iron, you should be able to solder the wires back on without any problem - assuming you are competent at solder work generally. Just don't apply heat for more than a second or so at a time, and you should be fine.
I have been soldering speaker wires for nearly 30 years now and never damaged one so I think they are pretty robust.
MkIIa, blue lit buttons, memory upgrade, 1Tb in Subaru Forester STi
MkII, 240Gb in Mark Lord dock
MkII, 80Gb SSD in dock