Well, I have no idea what your picky kid will and won't eat, but i'll give you a list of our go to snacky and lunch pail things that we use for our gf kids and you can pick and choose if any work for you.
nuts (peanuts, cashews, pecans, almonds and whatever else we have on hand), mixed with whatever the individual kids prefers (raisins, other dried fruit, chocolate chips, shredded coconut, etc)
muffins. I pretty much make a batch of muffins daily of a wide variety. These are go to's for school snacks and lunches as well as after school snacks.
rice cakes, topped with peanut butter or something else that the child prefers.
raw veggies. My kids love red pepper, carrots, cucumber, sugar snap peas
cut up fresh fruit.
Applesauce.
Larabars or other gf/df snack type bars.
corn chips and guacamole.
This is all stuff that we use for packed lunches and school snacks. Meals prepped to be eaten at home obviously offer much more flexibility.