Peel shrimp, leaving tails intact, and devein, if desired; set aside.
Combine ginger and next 9 ingredients in a food processor. Process until well blended, stopping to scrape down sides.
Thread 2 shrimp onto each of 12 (6-inch) skewers. Measure 1/4 cup peanut sauce, and brush on shrimp. Reserve remaining sauce. Grill, covered with lid, over medium-high heat (350° to 400°) 3 minutes on each side or until done. Serve with reserved sauce.