If you're shooting clays close enough that this question seems logical you might seek a better thrower. I wouldn't use a starter pistol to shoot clays but I wouldn't put the barrel to my eye and pull the trigger.
Lightweight projectiles rapidly decelerate but at close range can penetrate the skin, etc. If you happen to have a copy of Di Maio's "Gunshot Wounds" 2nd ED take a look at page 219. Polyethylene and polypropylene filler used in some buckshot and birdshot shells penetrated facial skin just fine.
Knight's "Forensic Pathology" states that the wad will stay with the shot column and likely enter the shot wound within 1-2 meters. 2-5 meters it will drop enough to create it's own wound, and after that the wad is unlikely to hit the body at all. Wad wounds are typically just abraded skin.
My personal opinion is the wad is probably going to be staying with the shot column at distances where it's likely to cause any significant injury, but wads and filler can cause some level of injury.