Instead of hands, they could use their claws. After all, they`re there for a reason, right? Unlike the hand-to-hand version, the claw-to-claw would damage enemies without needing to reduce their fatique below 0. I found a video in youtube that slightly resembles as to how I would envision this working.
http://www.youtube.com/watch?v=hFKgFQXThfY
Now I`m sure some would say that this paw-nage would be overpowered compared to the already underpowered hand-to-hand combat but according to the lore khajiits are supposed to be better at hand-to-hand anyway.