Won't this trigger both when you activate the first ability and when it's saved from death? I mean, the first instance wouldn't do anything, but it still goes on the stack.

Honestly, I don't know. I thought that things that trigger on rengerating only happened when the "regeneration shield" took effect.

Check out the Oracle wording on Matopi Golem or Soldevi Sentry:

": Regenerate ~. When it regenerates this way, it deals damage equal to the damage removed from it to another target creature or player"

It's weird to reference the damage. I would just have it deal 2 damage I think.

I had it worded that way so that other things regenerating it would matter, but your wording is more sensible.