How to Make It
Stir together chicken, cheese, and wing sauce in a medium bowl. Set aside.
Whisk together eggs and water in a shallow dish. Whisk together flour and salt in a separate shallow dish.
Working with 1 wonton wrapper at a time, place 1 to 2 teaspoons of the chicken filling in center of wrapper. Dip finger or brush in egg mixture, and brush lightly around edges of wrapper. Fold wrapper over filling, forming a triangle, pressing to seal edges. Set aside, and repeat with remaining filling and wrappers. Do not discard egg mixture.
Preheat oil to 350°F in a Dutch oven over medium to medium-high. Lightly dredge stuffed wontons in flour mixture, and then dip in egg mixture, letting excess drip off. Coat again lightly in flour; dip in egg, and lightly coat in flour once more, creating a double breading. Fry in small batches until golden brown and flaky, flipping occasionally, about 2 minutes. Drain on a paper towel-lined plate. Repeat process with remaining pieces. Serve immediately with celery sticks, and buffalo sauce and blue cheese for dipping. (Alternatively, drain on a rimmed baking sheet lined with a wire rack and keep warm in a 200°F oven until ready to serve.)