Prepare either a grill or a heavy skillet over high heat, remove the salmon from the marinade and cook until barely soft to the touch (about 4 minutes each side). Reserve and keep warm. Sautée the shiitakes over medium heat with about cup dressing until barely warmed, about 3 minutes. Remove and set aside to cool. Combine all ingredients except the wonton, rice stix and salmon in a large bowl and toss with the dressing. Allow 1/4 cup per serving. When ingredients are well coated with dressing, gently toss in wontons and rice stix, as these will only remain crisp for a short period of time. Arrange salad on a large plate and top with grilled salmon.
Dressing: Combine all ingredients except oils in a mixing bowl and whisk together well. Slowly pour in oils while continuing to whisk.