Using a damp cloth, gently clean mushrooms. Remove stems and discard.
Mince onions and separate white and green parts.
Preheat an air fryer to 360 degrees F (182 degrees C).
Combine cream cheese, Cheddar cheese, the white parts from the scallions, paprika, and salt in a small bowl. Stuff filling into the mushrooms, pressing it in to fill the cavity with the back of a small spoon.
Spray the air fryer basket with cooking spray and set mushrooms inside. Depending on the size of your air fryer, you may have to do 2 batches.
Cook mushrooms until filling is lightly browned, about 8 minutes. Repeat with remaining mushrooms.
Sprinkle mushrooms with scallion greens and let cool for 5 minutes before serving.