One thing, Katanas make for really bad anti-zombie weapon.
They were designed for swift draws and are not really durable, repeated use in a zombie apocalypse will continuously wear it down eventually becoming dull or get chipped. They are also hard to maintain, really hard to maintain and it requires a really skilled hand to use properly and not cut yourself.

I am not trying to hate on your choice, but realistically, it's not a great weapon.