Slice the beef into 1/8-inch-thick strips. In a container, combine the coconut milk, ginger, curry paste and soy sauce. Add the beef and toss to coat. Chill for 3 hours.
Meanwhile, in a bowl of water, soak 24 wooden skewers for 30 minutes.
Preheat a grill to high heat or a grill pan over medium-high heat. Thread 1 beef strip onto each skewer, weaving in and out at 1-inch intervals. Coat the meat lightly with cooking spray and grill, turning once until no longer pink, 45 seconds per side. Serve with lime wedges.