Charon knew in the back of his mind (and the middle of it, and the front, too) that it was a bad idea to agree to go and meet Ate. However, if she knew where Melinoe was and was willing to tell him in exchange for him coming, then he'd go.
Generally speaking, he wasn't a violent person. He'd spent most of his life in the Underworld, not doing much more than transporting shades. But once he'd found himself topside, he hadn't had much to do anymore, except on occasion. So he'd started trying out hobbies, and he'd found that he'd had a knack for boxing, and that had led to him studying Muay Thai and Jiu-Jitsu. If nothing else, it passed the time and kept him in shape.
He found the address that Ate had given him, and made his way to the open door. He pushed it open a bit further with two fingers before walking inside, warily taking in his surroundings.