I would clean all the metal before soldering - it's difficult to solder onto corrosion and the rosin in the solder probably won't be enough to get it clean. A flux-pen might be sufficient, though I doubt it. Otherwise a drop of mild acid like vinegar can work but needs to be completely neutralised afterwards with bi-carb of soda and a rinse.
Looks like a rivet is missing? Whatever replaces it would need to be solder-compatible - solid (not plated) brass ideally. A new hollow brass rivet or, if not available, a short length of brass or copper tube or even a brass screw perhaps, depending on how original you want to keep it.
The body is possibly Bakelite? If so, it'll start to decompose around 300C, which means soldering shouldn't be a problem if done reasonably quickly. Lead/tin solder works at a lower temp than lead-free, so another good reason to use the poisonous stuff. Bakelite cracks fairly easily under tension, so rivets etc should be sloppy fits in the diameters of the holes, not tight.