Does using Shadow Kill lower your chaos level?
Solution 1:
No. As far as chaos is concerned, kills are kills, so long as it happens by your hand.
(Now luring guards and weepers into conflicts with each other, that's fair game.)
Solution 2:
You will still get chaos from the kills. However kills are not the only source of chaos, found unconscious or dead bodies generate chaos too. As this skill makes dead bodies disappear, it will definitely help lower the chaos, if you are playing lethal.