Well I went to the Lord Regent's bedroom to get the confession to bring to be broadcasted, and he was in the room. I waited and waited on his balcony, but he wouldn't leave the room. He walks onto the balcony so I sleepdart him,get the confession from the safe and am on my way back to the broadcast control room. Will I a favorable result or do I have to go back and finish him off?

As long as he's unconscious, you should get the non lethal result.