Are the rings on this website what you are talking about?
I sometimes work with a woodturner to create silver and wood boxes.
We don’t make rings, but your description made me curious so I took a
look at them.
This pure guess work on my part… and I could be way off. It
appears the silver and wood is riveted together. In several of the
designs you can see tiny darker color metal circles at four points. I
would guess that a sandwich is made using a combination of CA glue
and rivets to hold the silver and wood together. Then the entire unit
could be placed on a lathe and refined to a smooth continuous
surface. Lathes have attachments that allow you to hold a piece from
either the inside or the outside, so it would be possible, by using
both, to smooth and refine all the surfaces.
Again, just guess work. Hope it helps! I’ll run this by Frank, my
woodturner buddy, and see if he has any ideas.