Although Weller is a totally different physical type from the actor who originated the role, it strikes me that Harry Mudd could easily be described as a businessman/CEO with his own ship. And if he is playing Mudd, perhaps the story combines both "Mudd's Women" and "I, Mudd" into a single tale, with Cumberbatch playing the android Norman. (Who, as I recall, also wore a Starfleet uniform, and was immune to Spock's nerve pinch.)