As for the game, there's always low chaos options, but as for cannon I can understand not wanting to kill him.
A popular fan theory that's going around is Daud being killed off and becoming the Outsider, which I wouldn't want to see (personally) as Daud is my favorite character and I'd hate to see him become the thing that he hates the most.
So, I can definitely understand where you're coming from.
As for the Outsider and giving powers, that's true, but I think Daud sees a pattern, maybe not blaming the Outsider for everything as it seems from the trailer, but The Outsider has certainly spawned his own chaos intentional or not.
I don't think that Daud is blaming The Outsider for the crimes that HE has committed, rather I think he sees a problem and wants to stop it.
The Outsider, even with the best intentions, interfering caused problems for everything else.
My guess is that it's probably directly linked to the Eyeless gang / cult and that they are not just Outsider groupies.
They seem to study the Void and may use the Outsider for their own plans.
Maybe the threat of a second Great Burning is enough for Daud to decide to kill the Outsider before that happens.