In a bowl, mix together the chopped chicken, minced garlic, mayonnaise, yogurt, hot sauce, and salt. Stir until everything is well combined.
Lay one tortilla flat on a clean surface. Sprinkle about 2 tablespoons of grated cheese along the lower third of the tortilla. Spoon about ⅔ cup of the chicken mixture on top. Add another tablespoon of cheese and a sprinkle of chopped green onion.
Fold in the sides of the tortilla, then roll it up tightly from the bottom to form a wrap. Repeat with the second tortilla.
Heat a non-stick pan over medium-high heat and lightly spray it with olive oil.
Place the wraps seam-side down in the pan. Cook for 3 to 4 minutes on each side, until golden brown and crispy. Cover the pan with a lid while cooking so the filling warms through.
Slice each wrap in half and serve hot.