I don't do any customising or major refurb works on any vintage figures, but is there a way to actually remove badly rusted screws properly?

Case One - Screw heads are badly corroded. Grooves for screwdriver gone. Are these beyond repair (breaking the figure is not an option)?

Case Two - Screw heads are badly corroded, but grooves are still visible. By the looks of it, if I use a screwdriver to try and get the rusted screw out; the (+) shaped groove will lose shape, turning this into a Case One.

Any tips, advice or knowledge would be awesome