Modern kendo teaches katana as a two-handed weapon, but Niten Ichi Ryu is specifically a two blades at a time school, so it teaches one-handed katana. Some other traditional kenjutsu schools taught katana as a one-handed weapon.
Fencing currently supports broadsword, rapier, cavalry saber, fencing foils, fencing sabers, fencing epees, umbrellas, canes, and cudgels. It should probably also support the cutlass and scimitar, as those are basically variations on the cavalry saber.
Niten Ichi Ryu currently supports katana, wakizashi, bokken, and nodachi. Letting it work with the scimitar, cutlass, and cavalry saber makes sense to me: there are differences between a cutlass and a wakizashi, but you could perform more wakizashi techniques with a cutlass.