its true cut damage do nothing to chain mail or plate.
Nearly no sword type weapons of the medieval age did any damage to those armors. Experienced through a good armor, 90% of the weapons we have in cRPG would get reduced to something heavy hitting your armor with different speeds and momentum..
Whatever energy got passed through to the wearer became blunt trauma. Plate just spread the shock over a bigger area. To actually kill someone like this would need a sharp thing like an awlpike for mail, or a long dagger through gaps in the armor. Or something very big and heavy like a hammer or huge axe to the head.. It all got translated to blunt damage through plate, mail and padding.
For all the swords, the only thing that would matter is how much energy you could project to the point of impact.
To me, except the range of it, the katana seems a sensible weapon. It's thick and solid enough to not bend when thrust through light armor or light mail, while the curve gives it a smaller cutting point than a straight weapon. It pays for these attributes in it's range, which is short.
In europe, take a classic longsword, they tried to increase range without adding more weight. They achieved this by adding groves to the blades, scraping off weight they could put at the tip instead. The swords payed for this in being less stiff and more bendable. Works excellent for duelling, peasants and portrait paintings, against armor not so much. For armor they developed shorter, stronger, blunter, more clubby weapons instead. (hammers, picks, flails, awlpikes and stuff like the goedendag)
TBH, using common sense I think the katana is closer to an anti-armor weapon than a longsword. Not by any means a weapon suitable for anti armor, but better than a long, thin, bendy blade.