Staffan: I'm not going to argue your impression of the RL or mythical katana, but, I will say that you probably need to familiarize yourself with the d20 mechanics a bit more thoroughly before you start messing with them. Modifying rules, and even something as simple stating out a new weapon using existing rules, can be tricky.
Take 3d4, for instance, with a max damage of 12 you might think it not excessively more potent than 2d6 or 1d12, but the average is actually higher. Or, look at the differences between martial and exotic weapons - you just don't see jumps from 3.5 average damage to 7.5 average damage for otherwise similar weapons (and that's the jump from a scimitar to your katana).