Preheat a grill to medium-high. Using a mini chopper, process 1/3 cup sugar with 2 teaspoons coarsely chopped candied ginger until fine; transfer to a plate. Brush 12 sea scallops with vegetable oil and toss in the ginger sugar. Thread each scallop onto a 6-inch skewer; season with salt. Cut 2 limes into 6 wedges each. Thread the lime wedges on top of each scallop, rind side up. Grill, turning once, for 5 minutes. Without removing the lime wedges from the skewers, squeeze the lime juice onto the scallops before eating.