Soak eight 6-inch-long wooden skewers in water, 10 minutes. In a bowl, combine orange juice, mirin, soy sauce, vinegar, chile, and ginger. In another bowl, marinate shrimp in 3 tablespoons sauce, 10 minutes.
In a large pot of boiling salted water, cook noodles according to package instructions. Drain and rinse noodles with cold water.
Heat a grill or grill pan to medium-high. Clean and lightly oil hot grill. Thread shrimp onto skewers. Cook, turning once, until shrimp are opaque throughout, 3 minutes. Serve shrimp and noodles with desired toppings and remaining sauce for dipping.