I would use the bat for the first swing and then discard it or let the opposition "take" it from me after he grabs it.
Everytime I've fought someone with a weapon, keeping the weapon was their main concern. I would just grab their weapon hand and start punching them in the eye with my other and they'd just take it.
They're like monkeys getting caught in the simplest trap because they won't release their grip
Knife in a landslide