In a small bowl, toss the shredded daikon with the ponzu sauce.
In a large nonstick skillet, heat the oil until shimmering. Add the shiitake and cook over high heat until lightly browned, about 6 minutes. Add the cabbage and greens and season with salt and pepper. Cook, stirring occasionally, until wilted, 3 minutes. Stir in the soy sauce, mirin and water. Arrange the fish over the greens and season with salt and pepper. Cover and cook over moderate heat until the snapper flakes with a fork, about 8 minutes. Transfer to plates and serve with the daikon and ponzu sauce.