Here are some tips for healthy snacks that can be included in a lunchbox. I usually make up large amounts, then divide them into snack sized zip lock bags so that the kids can grab and go.
Most schools have a "No Nuts" policy, so be keep the nut snacks for home.
Finger food veggies - cucumbers, carrots, capsicum, cherry tomato's, beans,
Olives (deseeded) / /
Muffins Here are 10 muffin recipes.
Bliss Balls - Here is the recipe to a nut free bliss ball.