yo /diy/, my 1950s house came with its original brass door hardware; trying to completely disassemble the doorknobs so I can remove all dirt and worn lacquer

the problem is that the doorknob is fastened to the backplate with a brass ring slightly larger than the diameter of the backplate opening. how can I remove this without damaging the doorknob?? (will provide some additional pictures for context)

two possible solutions I can think of:
1) cut the brass ring with a fine saw, gently bend and remove it. after cleaning, reinstall the ring and solder the cut
2) remove the ring with pliers and discard. after cleaning, replace with a new brass ring slightly larger than the old one, then compress around the doorknob stalk (???) with some kind of specialized tool

If option 1 is the best, then what tool do I use to cut and remove the ring? A jeweler's saw would be appropriate for the size and material I'm working with, but it's not the right shape to reach the brass ring without damaging any other parts

If option 2 is best, then what's the name of the specialized tool I would need to buy?

Is there some third solution I'm not considering?