Combine shrimp, 2 tablespoons sake cooking wine and sesame oil in a bowl.
Let stand 20 minutes. Preheat grill. Thread 5-6 shrimp on each skewer (reserve marinade). Grill shrimp about 2 minutes per side, turning with a spatula to release from grill.
Stir reserved marinade, remaining 4 tablespoons cooking wine, juice, soy sauce, ginger and cornstarch in a small saucepan. Simmer 1- 2 minutes until slightly thickened.