I would try to find out what other parents are sending. If all of his classmates are eating fritos, chips or other snacky types of food that you don't allow at home or in his school lunch, he will be less likely to eat what you might have packed. Doesn't mean that he won't eat what you will send, it just means that perhaps he could have a "freebie day" where forbidden foods are allowed. If the school or the teacher have not supplied you with a list of foods that can not be in the classroom due to allergies, ask. Peanuts are not the only food to cause severe life threatening allergies.
I second or third the cheese cubes and crackers. yogurt to go things can be frozen and even if they are crunchy are good to eat. Carrots/veggies with dipping sauce (my kids liked ranch dressing) is a big hit. Trail mix - those without the nuts are good things too. Applesauce to go squeezable packages are fun, but may end up in that mess or fight with others. If he is used to eating pita chips that can be a replacement for potato chips. Also be aware of any irritable bowel type of reactions to foods, you don't want him to be embarrassed by a need to use the bathroom when it is not a scheduled classroom break.
If the majority of his classmates are eating school lunch he will want to eat it too. The lemmings factor thing, even if it isn't good, to standout and not have school lunch is difficult for any child. And be prepared for the lunch bag to be left or lost. Preschool teachers are often more aware and patient with gathering supplies/possessions at the end of the day (due to student/teacher ratios) than K teachers. K teachers are angels, but in today's environment may have up to 30 kids in their classroom.