I would avoid juice boxes at AK, as they have plastic straws which are prohibited for the safety of the animals. We do regularly bring in small snacks and frozen water bottles with us.
Can food be brought into Walt Disney World Resort hotels and Theme Parks?
Guests are allowed to bring food itemssuch as snacks or foods that do not require heatinginto any Walt Disney World Resort hotel. If you have food items that need to be refrigerated, please ask the front desk at your hotel to have a refrigerator placed in your room. Refrigerator may require an additional charge. Guests are allowed to bring food itemssuch as snacks or foods that do not require heatinginto any Walt Disney World Theme Park. Inform a Security Cast Member of any food items when you enter the Theme Park. Learn more on our Special Dietary Requests page.
It's probably just easier and quicker through security if you do in terms of bag checks. I don't think you'd get in trouble if you forgot to mention the sandwich in your back pocket.