The kinetic energy in the ball's motion when it returned to her face should have been no greater than that imparted by the "slight shove". Can't have been so very slight. (Or else leaving a mark in the wall was easier than it sounds.)

I just tried thwacking my nose with about as much force as I could reasonably describe as a "slight shove" in that situation. It wasn't terribly pleasant, but it wasn't very painful and did no damage.

I cordially doubt that the younger prof was in danger of anything very bad. Assuming that the rest of the story is true, I suspect that Feynman was either being (commendably) over-cautious or showing off. Perhaps both.

(There's a more unpleasant failure mode for this demonstration: If you move your head forward after releasing the ball, then it'll hit your nose earlier, when it's lower down, which if the ball is very heavy can mean quite a considerable amount of extra energy.)