Whisk the butter, hot pepper sauce, and vinegar together in a bowl until smooth. Stir in the shredded chicken, and let stand 15 minutes.
Lay out several wonton wrappers, place 1/2 teaspoon chicken in the center of each wrapper and top with 1/2 teaspoon cream cheese. Brush the edges of the wonton wrappers with egg white, fold them over the filling in a triangle shape and press the edged together to seal. Continue until all of the wontons are filled.
Heat the oil in a saucepan over medium-high heat to 375 degrees F (190 degrees C).
Cook the wontons, carefully placing the wontons 4 to 5 at a time into the hot oil and deep fry until golden brown, flipping as necessary for even browning, about 2 minutes. Remove the wontons from the oil and drain on paper towel.