The broadcaster could run a bot with a trigger command that can perform the mod command, allow only that one user.
Or you could do something I’d find slightly crazy, like broadcaster can make a web interface (php works) that uses the chat oauth token(of the broadcaster) to socket (using php) to the chat and perform the command as the broadcaster. This method would require more work of course, like a twitch auth to verify who the user is logging into this interface to make sure it’s secure.