How to Make It
In a large bowl, mix together the shrimp, mayonnaise, bread crumbs, egg, horseradish, chives, 1 teaspoon salt, and ¼ teaspoon pepper. Form the mixture into 8 patties. Chill until firm, at least 30 minutes.
Heat 3 tablespoons of the oil in a large nonstick skillet over medium-high heat. In 2 batches, cook the patties until cooked through, 3 to 4 minutes per side.
Meanwhile, in a second large bowl, whisk together the vinegar, the remaining 2 tablespoons of oil, ½ teaspoon salt, and ¼ teaspoon pepper. Add the greens, tomatoes, and radishes and toss to combine.