This mission is probably the easiest out of all of them, but regardless there are a few things that will make life much easier for a stealth approach. This guide explains how to rescue emily non-lethally and undetected.
In this mission you can either assassinate Daud or you can send him a message by stealing his belt pouch and leaving him alive. I certainly prefer the latter option, and you have to do it that way to complete this mission non-lethally. This guide explains how I completed this mission non-lethally and without being detected.
Quick note: you go to this area multiple times. The first is when you eliminate high overseer campbell. The second is in the House of Pleasure quest where you rescue emily and eliminate two brothers that are fairly powerful. This is a guide for the second time you go there, the secrets and locations of the bone charms and runes are different each time you enter an area.
There are a few bone charms and runes around the place. There is one in Dr. Galvani’s house, 3 in the streets and apartments in the Distillery district and one inside the Distillery. There is also a secret where you help a woman escape from some guards.
In the end I didn’t actually not kill anyone. I have no idea who I killed, but the quest summary said I killed 2 enemies. But I still had a low chaos rating so the 2 kills only really impact my pride. Anyway, this guide explains how to eliminate High Overseer Campbell non lethally and indeed all enemies non lethally and without being detected. There are a few secrets in this area, I also talk about where those are located.