1. Toss together crab, pork, scallion, mint, ginger, soy sauce, and sesame oil in a small bowl for filling.
2. Dust a baking sheet with cornstarch; set aside. Working with 4 wonton wrappers at a time, arrange on a clean dry work surface and place about 1 teaspoon filling in center of each. Brush wrappers around filling and out to edge with egg. Bring 2 opposite corners of wonton together to form a triangle; firmly press edges together to seal. Arrange on prepared baking sheet. Repeat with remaining wontons, filling, and egg.
3. Heat vegetable oil in a large heavy saucepan over moderate heat until a deep-fry thermometer registers 360 degree F. Fry wontons in batches of 8, turning, until golden brown and cooked through, about 2 minutes per batch. Transfer with a slotted spoon to paper towels to drain. Arrange cooked wontons on a platter and serve warm or at room temperature with chili sauce on the side for dipping.