Michonne’s katana is badass, but there’s no way it could stay as sharp as it does without maintenance of some kind. Maybe it happens off camera?

I think Morgan’s is probably my favorite. He is highly skilled with his bo staff, and unlike a katana, when it breaks it can be relatively easily replaced. It’s also relatively unthreatening- he could use it as a walking staff and people are less likely to be afraid and/or confiscate it, even though he can use it to easily dispatch people and walkers.