Place radishes in a small bowl. Bring white wine vinegar, sugar, red pepper flakes, 1/2 tsp. salt and 3/4 cup water to a simmer in a small saucepan over medium-high heat and cook, stirring occasionally, until sugar is dissolved, about 5 minutes. Immediately pour brine over radishes and let cool, Cover and chill at least 2 hours,
Meanwhile, rinse rice until water runs clear. Combine rice and 1 1/2 cups water in a medium saucepan, season with 1 1/2 tsp. salt and let sit 30 minutes.
Bring rice to a boil. Reduce heat to low, cover and cook until rice is tender, 18-22 minutes. Remove from heat and let sit (still covered) 10 minutes, then fluff with a fork... keep warm.
Soak hijiki in 1/2 cup cold water in a small bowl until softened, 10-12 minutes. Drain; set aside.
Bring a medium pot of water to a boil; season generously with salt. Add shrimp, cover pot and remove from heat. Let sit until shrimp are cooked through, about 3 minutes. Drain and transfer shrimp to a bowl of ice water; let cool Drain and pat dry; cut into 1/2" pieces. Set aside.
Whisk shallot, soy sauce, gochujang, rice vinegar, fish sauce, honey and oil in a large bowl. Add reserved hijiki and shrimp to honey-gochujang dressing; toss to oat. Cover, chill 1 hour. Taste and season with more salt if needed.
Divide rice among bowls and top with shrimp mixture, drained pickled radishes and mizuna or arugula. Sprinkle with sesame seeds.