I'm almost sure that I saw on a footage, when scorpion was changing styles, the Mugai-ryuu name when he equipped his sword.

On the same footage, it seems that scorpion has no attack using both hands to hold the sword.

Since I've practiced this kenjutsu style, I've found out some strange things:

-It's true that Mugai-ryuu has lots of Katatewaza(one handed techs), but not all the way through.
-Mugai-ryuu uses katana as weapon, not a straight sword like the ninja-tou.
-Mugai-ryuu is a kenjutsu style, created by poor samurai. There's no reason for a ninja to use it(if scorpion is a ninja)

So it makes me think why the MK team chose this style for scorpion. Maybe randomly? Anyone knows?

Oh, by the way, for Shinsengumi and Rurouni Kenshin lovers, Mugai-ryuu was one of Saitou Hajime's kenjutsu styles