In a large bowl, combine the finely diced chicken, finely diced shrimp, diced green onions, minced cilantro, 1 teaspoon minced garlic, 1 teaspoon minced ginger, minced serrano (seeded), 1 1/2 tablespoons soy sauce, 1 tablespoon sherry, 1 teaspoon cornstarch, 1 teaspoon sesame oil, 1 teaspoon crushed red pepper, a dash of salt and pepper, and a pinch of sugar; mix until evenly combined.
Cover the filling and refrigerate for at least 1 hour or up to overnight to chill and firm the mixture.
When ready to assemble, place a wonton wrapper on a clean surface and put a heaping teaspoon of filling in the center; fold or tuck the wrapper sides to seal the filling and form the wonton. Place completed wontons on a parchment-lined tray and refrigerate for 1 hour to chill.
Make the dipping sauce by pureeing the sauce ingredients (1/2 cup ketchup, 1/2 cup water, 1/4 cup white vinegar, 1/4 cup sugar, 1 tablespoon chili garlic sauce, 1/2 teaspoon soy sauce, 1/2 teaspoon sesame oil, 1 teaspoon minced garlic, 1 teaspoon minced ginger) in a food processor until smooth, then pour into a saucepan and bring to a boil over medium heat, stirring constantly until slightly thickened; keep warm.
Heat oil in a deep-fryer or heavy pot to 375°F (190°C). Fry the chilled wontons in batches until golden brown and crispy, then remove with a slotted spoon or tongs and drain on paper towels.
Serve the crispy wontons hot with the prepared dipping sauce.
