I'm going to guess this is your first kid. Most folks including myself fret over the first one. After 2-3 or more you realize how tough and resilient they are.
He would have to shoot thousands upon thousands of rounds for the lead to be a real danger. I don't know where you live but if you buy products also sold in California almost everything says it contains lead or other substances that are hazardous to your health and known to cause birth defects.
Lead is a definite danger but to try and totally eliminate all contact is futile. Better to teach your son basic safe practices. Don't eat or drink while handling lead. Stay upwind or if shooting indoors make sure there's proper ventilation. Wash up after shooting including your face. Life has enough worries just use common sense hope for the best and don't sweat the small stuff.