Whisk together garlic, lime zest and juice, sauces, ginger, and oil in a small bowl. Toss shrimp and zucchini in a medium bowl with 1/4 cup sauce mixture to coat.
Heat grill to medium (350° to 450°). Cook noodles according to package directions. Drain, rinse under cold water, and chill until ready to use.
Thread shrimp and zucchini alternately on 8 metal skewers (8 to 10 in.). Oil cooking grate, using tongs and a wad of oiled paper towels. Grill skewers, turning once, until shrimp are cooked through and zucchini are tender-crisp, about 7 minutes total.
Whisk vinegar into small bowl of sauce mixture to make salad dressing. In a medium bowl, toss mint, butter lettuce, rice noodles, cilantro, and red onion with dressing until coated. Divide salad among plates and set skewers alongside each serving.
Note: Nutritional analysis is per serving.