Kensei fills the flavor of the later period unarmored duelist samurai, but I think what OP and I are talking about is more the Sengoku period full armor soldier samurai aesthetic, which is admittedly very close to Fighter in the first place, which is why I propose it as an archetype that trades Vanguard for a modified Tempest, and replaces Defender with the Samurai tree.
It's true that katanas are not a different weapon type in DnD though. In most editions they are just bastard swords, and we already have graphics for short swords, long swords, and bastard swords that fit both the straight and curved blade aesthetic, save for one detail: the tsuba. But if they did an Oriental Adventures inspired Kara-tur adventure pack or expansions, they could introduce new graphics for the same weapon and armor types we already have.
If they are going to add a new weapon type, I want to see polearms (spears, lances, poll-axes, halberds) which would lend itself to Cavalier/Knight, even if it has to be done like Inquisitive's dual hand crossbows, where the tree transforms a quarterstaff or whatever into said polearms. It's been so long without an addition to weapon types, I fear there may be a coding reason beyond "it's too much work to add new named items across all levels."
Whips would require an even deeper investment in animations and such, but hopium springs eternal that the chain attack can be built upon.