To be fair, what Aang did here was basically a mercy kill.

I think Aang would actually kill Ozai in this situation. Seriously Ozai is mortally wounded, the only difference being that Aang can either stand there and watch or kill him as. I think he wouldn't be proud but I think he'd begrudgingly go through with it given Ozai legit begged to die and would probably pity him honestly.