Combine pork, shrimp, egg, green onions, ginger, soy sauce, cornstarch, wine, sesame oil, salt, and garlic salt in a bowl. Mix filling well.
Separate and place wonton wrappers onto your work surface. Spoon about 1 1/2 teaspoon of the filling onto the center of each wrapper. Use your finger or a pastry brush to lightly moisten edges of wonton wrappers with water. Fold one corner of the wrapper over the filling onto the opposite corner to form a triangle. Press edges together to seal.
Bring 2 quarts water to a boil. Add wontons; cook until they float to the top, about 5 minutes. Reduce heat to medium-low; cook until pork is no longer pink, about 5 minutes more.