In a non-reactive shallow pan, mix together 1 cup teriyaki sauce and 1 cup water for a marinade. Place the salmon on the pre-soaked skewers and marinate for 10 minutes.
Heat oil in a grill pan or non-stick skillet over medium-high heat. Grill the skewers for 3 minutes on each side for medium, or 5 minutes on each side for well done.
Arrange the skewered salmon in a star-like pattern. Generously drizzle 1/2 cup teriyaki sauce over the skewers. Garnish with sesame seeds and green onions.