So, I'm doing my low-chaos playthrough. And now I'm in the Flooded District. I know I'm going to have to deal with Daud, but I'm not sure of the non-lethal way, if there is one. Someone help me out? How do I take care of Daud without killing him or too many of the men guarding him?

Well, there are two options.

One is just sneak behind him and take the key from his desk and blink out. You can also pickpocket him if you like. He has a Bone Charm on him.

Another is to actually engage him in a fight. I did this on my first low chaos game, and I highly recommend it if you don't mind getting detected and killing a few of his henchmen. I won't spoil too much, but the fight will eventually come to a conclusion where you can choose Duad's fate. Might be my favorite part of the game.

3rd option: wait until the guard reporting Corvo's disappearance leaves Daud's office; take him out with a sleep dart or choking (but watch out for another guard on a crumbling building, watching the area - and if you have to sleep dart him, be aware he can topple forward and die - so no good if you're doing Clean Hands).

Then wait for Daud to do his 'regret' speech, and when he's not looking choke out the single guard that's with him, dragging the guy backwards so you're not spotted. When Daud stops talking he should go stand behind his desk facing forward. Blink in and pickpocket him and grab the key. This of course also works for the Mostly Flesh and Steel trophy/achievement as well.

And Save Game often!!!