Whisk together all of the vinaigrette ingredients and let stand for 1 hour before using. Shake well just before using.
For the pickles, place the cucumbers on a parchment-lined baking sheet and sprinkle with salt. Let them sit for 30 minutes, then pat dry with paper towels. Whisk together the sugar and rice wine vinegar in a bowl until the sugar dissolves. Add the cucumbers.
Rinse the rice in cold water and drain three times. Place the rice and water in a saucepan, bring to a simmer, cover, and cook until the grains are tender, about 20 minutes.
In a small bowl, combine the rice wine vinegar, sugar and salt until the sugar and salt are dissolved. Season the cooked rice with the vinegar mixture.
To make the mango-coconut dressing, purée all ingredients in a blender.
To assemble the salad, in a large bowl, toss together the sushi rice, vinaigrette, cilantro, carrots, scallions, edamame, and sesame seeds. Season with salt and pepper.
To serve, divide the rice salad between bowls. Top with diced salmon, pickled cucumbers, mango dressing, radishes and pickled ginger.