No, this is one of the few "additional effect" weapons that is not synthed using Alchemy. It is indeed Smithing, just like it's younger cousin the Kyofu (lvl 13, add. ef.: wind dmg).
I believed it was Alchemy, as well, but when I was unable to make either of these, I had to commission a Smith to create them for me.
...thanks for sharing. I'm sure that's exactly what they had in mind when they were naming this weapon.
It has nothing to do with the fact that —ó•—(reppuu) means "strong wind" or "gale" in japanese. Hey look, it uses a wind fan and does wind damage too. No wait, you're right, it's a finnish school bag.