Prepare grill. Soak skewers in warm water for 20 minutes.
While skewers are soaking, thinly slice garlic and in a shallow glass dish stir together with ginger root and 1/4 cup lime juice. Season marinade with salt and pepper. Holding a knife at a 45 degree angle, cut steak crosswise into about 1/4-inch-thick slices and add to marinade, tossing to coat well. Marinate steak at room temperature 10 minutes. In a small bowl whisk together hoisin sauce, ketchup, and remaining lime juice and season with salt and pepper.
Drain skewers. Beginning at one end of each slice of steak, weave a skewer lengthwise through it, stretching slice on skewer to flatten. Transfer to a plate. Season sates with salt and pepper. Grill sates on an oiled rack set 5 to 6 inches over glowing coals 30 seconds to 1 minute on each side for medium-rare.
Serve sates with hoisin sauce and lime wedges.