Almost nobody picks the katana. Even the people who pick it mocking the sword!
I can't really blame them because they didn't give you the option to pick the complete set for the katana to shine. If you use it with fedora you can teleport behind the zombies and kill them!
Nobody knows that the katana has this hidden skill bonus if you use it with fedora because this hidden mechanic only passed to the few chosen people in the secret society hidden under the house that people like to call "the basement"
If we're going on "brain damage to kill" rules you're going to need to clean sweep their head off or find a way to the brain. As cool as it is, that's a big ask for something designed for one swift body shot. I'd look for the spear since it's the most effective peasant weapon and be real, we're all about peasant skilled.