Preheat the oven to 350°F (177°C). Grease all 24 cavities of a mini muffin pan.
Press one wonton wrapper into each cavity. Lightly coat the wrappers with cooking spray or oil.
Bake the empty shells for 6–8 minutes, until golden, dry, and rigid. Watch the pointed edges closely.
Meanwhile, combine the room-temperature cream cheese, sour cream, garlic, four green onions, soy sauce, sugar, mozzarella, and crab in a medium bowl. Mix evenly.
Divide the filling among the pre-baked shells, placing one heaping Tbsp in each cup.
Cover the pan with aluminum foil. Bake at 350°F for 10–12 minutes, until the filling is hot and bubbling.
Immediately transfer the cups to a wire rack or paper-towel-lined plate. Garnish with the remaining green onion and serve warm with the optional sauces.