Would need to add a specific ruling that it can be finnessed while two handing... though I would argue shifting it to dealing 1d10 damage, 18-20/x2 would make them a solid weapon.
But yeah, I could see that as a katana. Though I would probably rule that the stats for a schimitar could also be called a katanna.
Well, if it's a 'realistic' katana, it's not all that finessable, but the finesse option itself doesn't really impact balance much. So yeah, keener, but lower base damage bastard sword should do.
As someone who did a bit of Kendo, i agree with the above. Katana's are not wielded with finesse, they're wielded as a proper blade. You don't make quick, successive, weightless attacks, but rather, you attack through power slashes. Each slash is meant to be lethal, and you're taught how to put the weight of your body into each blow, swinging your hips and forwarding your torso. Sure, with training you can do it faster and faster, but this is precisely what's covered by BAB anyway.
That said, Katana's aren't any sharper than european swords, this is a flawed comparison that was popularized by a century of Samurai movies that romanticized both the sword and the warrior.
Katana's were generally expensive in Japan, because iron there is much rarer, and it comes in powdered form, or "iron sand" (tamahagane), instead of the iron veins that are common throghout Europe, which are much easier to work with. Because their iron is harder to work with, swordsmiths had to get creative to get the most out of what they had, and the folding steel technique, the soft iron core with hardened steel outside, and the curved blades, were all adjustments made to increase the efficiency of the sword. European swords on the other hand were made of generally superior steel, in crucibles, which also had the ability to achieve greater temperatures than the fanned ovens of Japan. The swords were heavier, and made with higher carbon content steel, which meaned a sharper edge and more weight behind each cut.
In my opinion, the Katana and the european Longsword/Bastard Sword are not sufficiently different to be awarded different statistics on D&D. Bear in mind that Katana's have a range of different sizes,from 60 to 73cm (According to Wikipedia), while the common Bastard Sword had a range from 100 to 122cm. So by that logic, a Katana would be more appropriately categorized as dealing the same damage as a Longsword instead of a Bastard Sword, with the caveat of being able to wield it with 2 hands for 1.5 strength on damage.