In a large pot of boiling salted water, cook pasta according to package instructions. Reserve 1 cup pasta water; drain pasta and return to pot. Add 2 tablespoons butter and toss until butter is melted; keep warm.
Meanwhile, in a large skillet, melt 1 tablespoon butter over medium-high. Add garlic and radishes and cook, stirring occasionally, until radishes are crisp-tender, 3 minutes. Add radish greens and cook until wilted. Season with salt and pepper, then add to pasta and stir to combine. In skillet, melt 1 tablespoon butter. Add shrimp, season with salt and pepper, and cook, stirring occasionally, until opaque throughout, 4 minutes. Add shrimp to pasta and toss, adding enough pasta water to create a light sauce that coats pasta.