There are multiple One Handed katana related styles. Although you would have to look on google for where to find them unfortunately.
There is a DCUO database that tells you where all gear and weapons are known to drop. Google that and see if you can find your katana that way.
You can get a katana style one hander from the vendor that sells lowbie pvp items at midtown/diamond district for heroes. Tech infused ninja blades drop from level 15 Batman mentor instances.
1h katana is bought at the PvP vendors in the Metro and Gotham safehouses. DW katana is a drop from Black Adam in the Kahndaq raid.