Also, the ER probably wouldn't need to resort to cutting a cock ring in the first place. It has no bones, just get some ice packs on it or worst case scenario do a controlled bleed on the distal portion.
That must be the case but at the same time it makes me wonder why titanium rings aren't made with the shatter resistant alloy, or why it's expensive to get a titanium wedding band that shatters easily but apparently titanium cock rings are common and affordable enough that there's an ER PSB out on it.
There actually are reasons you want an alloy to break easily, street signs are designed to do this to minimise vehicle damage in a crash while still providing resistance to halt the vehicle as an example.
As for the cock rings, if you asked the metal shop owner that got commissioned for it, they'll get a thousand yard stare before commenting that it isn't even close to the most "intimate" custom order they've been paid for.
Titanium camping cutlery definetly doesn't shatter, it bends like steel. But it does scratch easily so maybe your rings used a harder alloy to prevent scratches