The ability to do so with all damage would be preferable. Or, at least, the ability to discriminate between sources/types of damage.
Well, like I said before I don't think there is a "simple" way (your quotes) to do what you want.
I did something similar using a cloak effect to hang an OnHit effect on actors around the PC. That works, but you'll find you get notified after the damage takes effect. So while you can heal the damage and then apply it to stamina, you can't do anything about one-shot kills.
The alternative is to edit every weapon, or every damage source in the game to do zero or minimal damage and then add a script to do the effect you want. you could probably do it with SkyProc and save most of the pain, although I'm not sure how feasible that is for traps and claws and so forth.
The third way would be to edit vanilla scripts directly I suppose, although that's not going to be compatible with a lot of other mods.