You can damage your hand; sleeping…
Actually; joking aside; the possibility of injuring hands while throwing yoyos is much less likely than most other possibilities.
Just about every single part of your body is just as likely to be the sad recipient of impact damage.
Most yoyos are hard flying objects(when you are throwing them; obviously). The yoyos are ‘mindless’. They only go where: you direct them or fail to direct them.
Crazy tricks… bad binds… moving faster than you can think… horizontal tricks(those are the tricks where you actually put your face ‘on the menu’ just by nature of the possible proximity paths to your above the neck areas.
You can smack yourself in the: nose, eyes, teeth, chin, forehead, top of the head, back of the head, in the elbow, in the temple, in the knee, on the shin, right in the crotch(not kidding), etc…
If it’s part of you; you can damage it while hurling around a ‘hard flying object’.
… The good news is that if you start with sensible yoyo playing fundamentals and don’t get ahead of yourself; you can absolutely minimize injuring anything.
There ‘is’ a possibility of injuring your hand or hands; throwing yoyos. Either from direct impact. Out from repetitive Movements over time. Or from long throwing sessions while having the string loop ;waaay too tight on your throwing finger. <> and a few other possibilities.
But generally speaking; throwing yoyos is much less likely to mess up your hands than many other pastimes.
I have no doubt that somewhere… there is a kid skateboarding downhill at night with Absolutely No safety gear whatsoever; that would suggest putting a string on your finger is dangerous🤔 Go figure…