Actually, I've done quite a few where you don't have a hand to slap with. You just use your feet, no big deal. But, it's a little unnerving the first few times. Just like falling with your arm on the outside instead of the inside. Sorry, don't know the Japanese name... or the Korean one for that matter, we just call it turn under twist to the outside.
There are no PERFECT techniques, only perfect execution for the situation at hand.