Pineapple Dole Whip is top eight allergen-free, though it does have a coconut-based ingredient. As someone anaphylactic to milk, tree nuts, peanuts, and seafood, which cuts out most dessert and snacks, pineapple Dole Whip is one of my go to snacks at WDW.
The Snack Safely website (
https://snacksafely.com/ ) has lots of info about snacks and specific products and manufacturers, which should give you some ideas for at home and travel.
I like the Enjoy Life brand (check out their website, they have more than just cookies and chocolate chips !!). At Disney restaurants, if nothing else they often will have Enjoy Life cookies as an allergy-friendly dessert option.
For MNSSHP, there will likely be some safe treats mixed in the bins at the treat stations -- e.g. when we went there were Skittles; I ended up with lots and lots and lots of little Skittles bags ;-) However, they are mixed in with the packages of everything else, so you would have to guage your comfort level on that.
But what MK also does is have the ability to get allergy-friendly treats (food and non-food) from guest services. In the past, you woudl go through the treat lines and get your bag of goodies, then trade in the not safe goodies for the safe ones at guest services. last year, they did a new way -- you can stop at guest services at the beginning of the evening and get a special Teal treat bag [may also be available at some treat stations], which signifies "food allergies" (see the Teal Pumpkin campaign by FARE). At the treat stations they will then give you a teal coin. You trade in the coins for the allergy friendly treats at guest services. It is not clear what they will do this year.
FYI, the FARE website has lots of great info for managing food allergies:
https://www.foodallergy.org/
SW