Put the dulse and wakame in a large bowl and cover with cold water. Let soak 5 to 10 minutes, until softened. Drain in a colander, pat dry and place in a serving bowl.
To make the dressing, whisk together the rice vinegar, sugar, ginger, wasabi powder, soy sauce and sesame oil in a small bowl.
Spoon half the dressing over the seaweed, add the lime juice and toss gently. Taste and add a small amount of salt if necessary. Surround the salad with the carrot, radish, daikon, cucumber and avocado. Season them lightly with salt and drizzle with the remaining dressing.
Sprinkle the salad with the white and black sesame seeds, pumpkin seeds and green onions.