I know you asked for a katana. But as a civilizd society pre-zombie apoc lets just have a little bit of a debate.
I don't like the idea of just a cutting weapon, if one were to use real world stats on slicing through neck bones, tendons and flesh then I don't think it would be that effective against zombies unless they were at an all time state of decay. Unlike some tv shows depict, I think a good blunt or spiked type weapon would be more valuable in a zombie apoc.
Instead I chose this as my zombie melee weapon.
Cold Steel Warhammer
I think given strength and the balance this would allow one to more easily dispatch zombies than a katana, and less chance of hurting yourself or over exerting the end user after a long hard days of zombie bashing. Plus it doesn't need sharpened and continually checked for damage. It is also easily repaired if you break the handle.
Also with a katana or any edged weapon, if one were to slice through the neck and sever the head from the body, then technically on a zombie the head is still alive and able to bite any unsuspecting people. I could see a person slicing off a few heads then stumbling to the ground under heavy duress of a lot of zombies and then getting bit by the severed head. Bad way to exit the zombie-apoc.