Mix water, wine, soy sauce and cornstarch in a bowl. Heat 1 Tb oil in wok over medium-high heat (add more as needed during cooking). Stir-fry ginger and garlic in hot oil for 30 seconds. Add carrot and sprouts; stir fry for 1 to 1 1/2 minutes or until crisp-tender. Remove from wok.
Stir sauce; pour into center of wok. Cook and stir until bubbly. Cook and stir 1 minute more. Return vegetables to wok. Stir to coat with sauce. Remove. Salt to taste. Cool. Fill wonton wrappers with mixture and wrap.