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.
Just like the safe in this area (I have written a guide for that too, click here for it) you find this by trying to find the Runes in the Flooded District Sewers Area using the hearth. This guide explains which is the better option and how to defeat Granny Rags should you choose to do so.
The combination for me was 528, your code may be different. You find this safe by finding a Bone Charm in the sewers area in The Flooded District, in fact the Bone Charm is in the safe. Next to the safe you find a letter with a story in it.
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.