Falchion Pure Monk?

[tenketsu2]

I like bizarre builds, and this is an idea that keeps seeming pretty attractive to me. Just /how/ crazy would it be to have a pure Monk that didn't use Ki weapons? By being uncentered you lose your stances, special ki attacks, 5 AC at 20(potentially?), and some to hit bonuses. But unless I'm missing something else, that's it. Now, that's a lot to miss out on, but could it be potentially viable anyway? You're gaining some potentially much better critical profiles and the ability to bypass DR without using kamas. For a monk, is this even close to an equitable trade off? Basically every complaint about Monk DPS I've read has been because of those two things.

If the idea isn't /completely/ unworkable, how would you build it? My thought, as the title indicates, is an Elven Falchion user as a sort of Samurai for aesthetics reasons, but you could just as easily go TWF Khopeshes.

EDIT: Fixed flat AC bonus reference