Either the bat is the hero’s sword in disguise, or his Swordsmanship Skill is so high, it turns any sword like object in his hands into things just as powerful as the hero’s sword.
"Excuse me sir. I believe you have a bat."
*Looks around* "A bat where", you reply.
"A BAT TO THE FACE", as you get smacked with a hard titanium bat wielded by a person who can throw cars.
*Bat sound from Smash Brothers*