Preheat your air fryer to 400°F (204°C).
In a medium bowl, stir together 2 cups cooked shredded chicken, 4 ounces cream cheese (room temperature), 1/3 cup buffalo sauce, 1/2 cup shredded mozzarella cheese, 1/4 cup sliced green onion, and 1/2 teaspoon garlic powder until well combined.
Place one wonton wrapper on a clean work surface. (Keep unused wrappers covered with a damp towel to prevent drying.)
Put a heaping spoonful (about 2 teaspoons) of the filling in the center of the wrapper.
Brush the edges of the wonton wrapper with a little water, fold the wrapper in half to form a triangle (bringing one corner to the opposite corner), press firmly around the filling to remove air and seal the edges. Repeat for remaining wrappers. (You can crimp the edges with a fork if desired.)
Spray the air fryer basket generously with olive oil spray. Arrange wontons in a single layer in the basket without touching; work in batches if needed to avoid overcrowding.
Lightly spray the tops of the wontons with olive oil spray.
Air fry at 400°F for 8–10 minutes, until the wontons are golden brown and crisp. Check at about 6 minutes and rotate or rearrange as needed for even browning.
Remove cooked wontons with tongs and serve immediately with ranch or blue cheese. These are best enjoyed right away, as they will lose crispness as they sit.