Dueling Mastery: Not saying no, not promising anything yet.
Dervish Dance: See Slashing Grace. Note that while neither of these feats really explicitly say it, they both thinly veil the fact that the weapons should be finesse-able. That said, dervish dance specifically applies to Scimitars, which are clearly not on the finesse list, and I happen to own 3 katana at home, none of which weigh more than 3lb out of scabbard (the 6lb as described by d20 systems is definitely inacurrate, possibly stemming from a confusion with the odachi). And if you ask me, by comparison to a european weapon of similar size and destructive power, katana definitely should be "finesse-able" to an extent, seeing as the cutting power actually comes from using proper technique to drive torque to the tip of the blade.
That being said, I can see why a line was drawn there between the katana and wakizashi, analogous to the split between long and short swords. So I'll go with RAW on this count, allowing Slashing Grace without the need for the weapon in specific to be finesse-able.
There's also the Effortless Lace + Agile route, though I doubt you want to spend that much/wait that long.