You can play the whole game without a single kill (well there's one spot that's being argued about) if you simply avoid most enemies. Imo though, that's something better done on a second playthrough, since it's much faster and you miss out on sneaky backstabbing fun.
Iirc, the quickest, non-lethal approach to the statue was to climb a pile of boxes outside, and then sneak around the guards to the top.
They aren't real people you know...I ended up killing a lot more than I would have liked, ...
I kinda liked the technology and setting of Invisible War...