Sunshine seasons has a vegan cupcake that was safe for our DD as well (DS is allergic to milk/eggs). At an ADR you can have an allergy free cake added at the podium (not sure if this is still offered, and we have not tried the dome cakes that are offered (see link below)). Usually the online menus will list treenut/peanut safe desserts. Our DD is allergic to peanuts, tree nuts, sesame seeds and sunflower seeds.
Resorts: The best cake she had was at Steakhouse 71 and they make it in house and the chef came to us and assured us there is no cross contamination (she reacted to a custom order cake that morning and didn’t want to touch anything-scary few hours)! At Art of Animation, she usually eats the mermaid cupcake. At Le Petit cafe (Riviera) she gets tarts/madeleines (check for cross contamination) and at Topolinos she can have the chocolate cake.
Epcot: Cake at the Honey Bistro booth has been safe for her. There are so many options. The first booth you stop at you can ask the chef about the desserts/snacks at other booths as well.
MK: Dole whip, pineapple upside down cake at Sunshine seasons, BOG dessert (they make sure to leave off the pearls/substitute a delicious chocolate ganache truffle; the speciality dessert now has a cupcake with nuts so it’s no longer safe); dessert party we filled a special form and they gave an overly sweet plate which neither kid ate much from, but there was banana bread, gummies, cheese, fruit. Halloween waffles at sleepy hollow
HS: ABC commissary has a strawberry shortcake dessert; milkshakes at Sci fi; chocolate cake at Hollywood&Vine
AK: the blueberry cake at Satuli is safe but NOT the chocolate (she had a violent reaction once; we were told it didn’t contain nuts but it actually has some hazelnut spread or something similar in it I believe. Churros at Nomad lounge; Lion king cake at Tiffins
If you truly want to be safe, you can order a cake from Erin Mckennas (as long as she’s not allergic to coconut; our Dd is ok with sunflower lecithin also) and they can deliver a cake anywhere on property (to resorts as well).
https://www.disboards.com/threads/official-disney-cake-chatter-part-v.3558085/
https://disneyworld.disney.go.com/guest-services/special-dietary-requests/
https://disneyworld.disney.go.com/guest-services/cake-orders/
Also, found these single dose diphenhydramine vials for traveling:
https://www.amazon.com/gp/aw/d/B07M93C4HP?psc=1&ref=ppx_pop_mob_b_asin_title
https://shop.allergysuperheroes.com/products/single-dose-liquid-medicine-bottles