Whisk dressing ingredients together in a small bowl. Season to taste with more salt and lime juice. Set aside.
Make salad: Put crab, radish, cabbage, hominy, cilantro, avocado, and half of green onions in a medium bowl. Add dressing and toss gently just to coat.
Divide salad between 2 or 4 plates, arranging some crab pieces and some radishes on top. Sprinkle with remaining green onions.