Nah, it would be fine. I'd also allow batted pucks, kneed pucks, headed pucks, whatever. As long as the player didn't close their hand on it, point that arm at the goal, ref.
Also get rid of the blue lines. Don't know why people hate scoring so much and love whistles and stoppages.
Kane was injured by a skate out by the blue line and it wasn't from a player trying to kick the puck. If you're trying to prevent that as much as possible I guess you need to get rid of the skates altogether. Injuries are a risk, there's no guarantee that a player would never get injured by a player trying to kick a puck into the net, but there's no reason to believe it would be an especially dangerous play.