I remember the first time I participated in a demonstration. We were near the edge of the mat when the nage threw me (I think it was a shihonage). I smacked my hand hard on the concrete floor next to the edge. OUCH!
In techniques where you "spin out" around tori who stays in center, I've gotten in habit of a different slap out. I'll pull my fist up to my shoulder with my bicep like I was hitting someone's face right by my shoulder and back fist the ground like that. Even when you really "loose your feet", spin out fast, and go down near horizontal it dissipates a lot of force. I like it because it keeps your hand near your head and helps you protect it and roll if needed. But, the kicker is, you back fist the ground with your knuckles. On a mat it works great. But I fear I'm going to fall and do it on black top one day and break a knuckle. Ouch