DoTs usually have more value the sooner they are applied, so maybe Hakaze -> Yukikaze -> Higanbana may be the way to go.
Higanbana's DoT may not be affected by the Slashing Debuff just like NIN's DoTs work, but it gets started way earlier than going the route of Hakaze -> Jinpu -> Gekko -> Higanbana.

I'm liking it that you get to choose what you want to begin with, if power or speed. Personally I would go for speed tho, with Shifu.