Stir cream cheese in a bowl until smooth. Fold in crab, green onions, Worcestershire, soy, garlic, sugar, salt, pepper, and sesame oil.
Heat vegetable oil in a deep skillet or pot to 350°F over medium heat.
Set out wonton wrappers. Place a heaping teaspoon of filling in the center of each wrapper.
Brush wrapper edges lightly with water. Press out air and pinch corners together to form a sealed pouch or star shape.
Fry batches of 5–6 wontons until crisp and golden, 2–3 minutes, turning once for even color.
Transfer to a wire rack or paper towels to drain. Rest 3 minutes to cool slightly.
Serve warm with sweet chili sauce for dipping.