nostr:npub1v7t4yx9vxtv3mat0hdsduuym4fvjd5dzmdlh82ssa40phr965h2s2lck6k nostr:npub1u83gudwdfwjngz5eqxkrnpvsuydvqwjxwz0majvehqrh62804hfq8yr2s5 thinnest saw i have is 0.6mm.  i'm sure you could order a thinner one but i suspect if you go much thinner than that you want a jig to hold the blade straight or it might break

as far as holding rings, i would just wrap the wire around a wooden or plastic dowel and cut lengthwise.

depends on your budget i guess whether you can justify a fancy tool.  but yea you have lots of options