Fruits and vegetables are the best option, but that is not always realistic. These are the snacks that are free of common allergens. I would strive for snacks with as few ingredients as possible. You don't need that many snacks. You just need a few that are slightly healthier than your current ones. These are some of our favorites:
Hain is a brand that doesn't process peanuts, so it is safer than most brands for children who have nut allergies.
Enjoy life is another brand who has a dedicated nut and gluten free factory. They are free of the 8 most common allergens and are perfect when children have different allergies. They make:
No Oats "Oatmeal" Cookie