Thaw shrimp, if frozen. For sauce, in a medium bowl stir together barbecue sauce, pineapple juice, oil, and ginger. Set aside.
Peel and devein shrimp, leaving tails intact. Thread shrimp onto 6 long skewers; brush with sauce. Grill shrimp on the rack of an uncovered grill directly over medium-hot coals for 10 to 12 minutes or until opaque, turning once halfway through grilling time and brushing with sauce the last 2 minutes of grilling.
Thread pineapple wedges onto 3 long skewers. Add pineapple skewers to the grill for the last 5 minutes of cooking, turning once and brushing with sauce halfway through grilling time.
Heat remaining sauce to boiling; serve it with shrimp and pineapple for dipping. Store remaining sauce, covered, in refrigerator for up to 1 week. Makes 6 servings.