The "platelets" you refer to are chitinous sclerites, different than cuticle. The chitin is covered by the waxy cuticle. The cuticle prevents dehydration.
Even the "flexible" parts tend to be covered with chitin. Only the joints between the sclerites are not hardened, but they are covered with cuticle usually. In fact, when insects molt, the sclerotized tracheae (breathing tubes) and the scleriotized foregut and hindgut are shed along with the rest of the exoskeleton. In other words, even the first part of the digestive system inside the arthropods are covered with chitin.
The "stuff" that protects mites is the same stuff that protects honey bees. The trick in applying a chemical is to apply enough to kill the mites without harming the bees; the mites develop some resistance, and the amount of OA that might have to be applied to kill Varroa might also be enough to kill or severely injure bees.