How about mini boxes of raisins, or mini bags of chips or popcorn - still not health food but several steps up from candy I think.
I don't have small children but I believe that both nuts and popcorn are not recommended for children under age 5. Major choking hazards. Candies would probably need to be checked on an individual basis.
I prefer to be machmir on "venishmartem meod al nafshotechem"
Nut and popcorn in most countries except USA are fair game including in security booklets requirement
I go to ST with bags to put the candies. Let kids be kids.