The silver of that time frame was very susceptible to uv, rain, etc.. and of course, the original lacquer is very thin. Be aware that to get past the oxydized level of paint, you will be *very thin*, and are likely to see 'thru' it to the primer underneath.... (but when I see primer peering thru very thin original lacquer, I see 'character'...

Maybe someone here will have a more modern suggestion, but you're probably not going to 'make it perfect'..
If you want to 'cut faster', you might try some 'rubbing' compound on the top surfaces, and I'd suggest using it by hand, so you can more easily stop before going too far... I'd rather leave a little silver even with spots than have no silver left at all...? Follow the rubbing compound with polish and I'd also put a good coat of wax over it once you find the right spot to stop..