In a small saucepan, add the ingredients for the teriyaki sauce, except for the cornstarch and water (slurry), mix well. Over low heat, simmer for 2-3 minutes. In a small bowl, add the cornstarch and water, and mix well, slowly whisk into the teriyaki sauce, cook for 1-2 minutes, or until the teriyaki sauce is thickened. Let cool for 2-4 minutes.
Place the salmon fillets in a shallow dish and pour the teriyaki sauce over them. Let them marinate for at least 10 minutes to allow the flavors to infuse.
Preheat your grill or skillet over medium-high heat. Cook the salmon fillets for 4-5 minutes on each side, or until the salmon is cooked through and flakes easily with a fork. Remove from heat and let it cool slightly before flaking the salmon into bite-sized pieces.
Lay out the lettuce leaves on a large plate or cutting board. Spoon a small amount of cooked white rice onto each lettuce leaf.
Place a portion of flaked salmon on top of the rice. Add garnishes on top of the salmon.
Sprinkle sesame seeds and sliced green onions over the wraps. Drizzle with sriracha if you like a bit of heat.