That's an unusual material for a ring, I just hope you don't get into the situation where it needs to be cut off. That would put me off using such a hard metal for rings and jewellery chains.
https://www.youtube.com/watch?v=poM423pewRE - “the home way”
https://www.loupe-magnifier.com/tungsten_finger_ring_removal... - “the professional way"
If you drop an endmill (like a drill bit but different, about the size of your thumb) from a normal carrying height to a concrete floor, you'll almost certainly be buying a new endmill; much like dropped buttered toast always seems to land butter side down, a dropped end mill always seems to land point down and crack a big chip off. A ring should be lighter so less stress, and smooth would imply no stress concentration points, but I'd still be careful about impacts or dropping it.
Another anecdote is interrupted cuts on a metal lathe will shatter carbide seemingly instantly every time, you need to use "old fashioned" high speed steel to cut anything with a gap. I wonder if the vibration of taking a diamond tip engraver to a carbide ring would shatter the ring instantly.
An interesting anecdote is a rather large lump of carbide for a replaceable indexable cutter is a couple bucks and a rod of carbide turned into a polished sharpened precision endmill of a large size is only maybe $30. Possibly the ring could cost more because that specific type of carbide looks very nice or has been stress relieved or annealed somehow to make it less brittle, and of course there's the labor time of a professional jeweler if its custom work. But the raw material, unlike gold or Pt, can't cost more than perhaps $100 for a carbide ring.