I'd fire him in a second with sufficient corroboration of the story. There's a non-negligible chance that such poor decision making isn't confined to just women.
With corroboration, I'd fire him in a second. You're opening your company up to a world of pain if one of your execs has a proven history of sexual assault. Furthermore, I know me personally would be looking for work elsewhere. I'm male, but I wouldn't want anything to do with someone I know has sexually assaulted a woman.