The switch is soldered with ROHS, which has a high melting point. Before trying to actually desolder the defective switch add some good ol' non-ROHS solder to lower the melting point of the original solder. Then use a solder absorbing tape. I've fixed 4 mice so far with zero failures, first one desoldered twice.
Many many thanks to the author for providing the part numbers of the replacement switches. Couldn't have done it without those.