I don't think Daud is a Thug. He is a stone-cold, disciplined & merciless killer -- but not a thug. He doesn't mindlessly go looking for trouble, trying to intimidate people. He runs his death racket in a tidy fashion and keeps under the radar as much as possible.
Compare him to Slackjaw, who is most definitely a thug.
As far as the moral paths allowable during the DLC, it's important to remember that you're playing Daud at a time where he's in transition. He's not so sure about his life path anymore. After his all the years of bloodshed, The Outsider has seemingly abandoned him. He's no longer special - and he's just killed the one lady holding Dunwall together. He sees his actions are leading to the widespread destruction of his world.
Normally, dispatching corrupt nobles wouldn't have an impact on him, but his last log entry is very telling. While ambition drove Daud down his current path, his self image has degraded to a point where he sees himself as rotten.
There is some remorse within him for some of the victims he has killed, who just happen to be the "just folks who were too just for their own good" -- those living in a world that's too corrupt to suffer them.
I think killing Emily was the final straw. It was easy to rationalise the consistent killing of those who svcked the empire dry for their own purposes.
But she and her father were widely considered as nobles who actually served for the good of the Empire. He tries to rationalize things and pin the blame to the Lord Regent. He tries pushing it on those who hired him to do their killing -- those who used him as their tool.
But it's just another step in the process as he tries to come to grips with where he has ended up in life.
His world is crumbling slowly around him. He's walking a tightrope above a sea of blood and filth, and he's running out of time. He knows his end is coming and he's trying to come to terms with how his life has panned and the man he has become.