Bring a large pot of lightly salted water to a boil. Cook fusilli in the boiling water, stirring occasionally, for 6 minutes. Add frozen vegetables; continue cooking until fusilli is tender yet firm to the bite, about 6 minutes more. Drain.

Soak the fusilli-vegetable mixture in cold water until cool to the touch.

Meanwhile, mix pickles, celery, and radishes with creamy salad dressing, Cheddar cheese, Thousand Island dressing, relish, and Dijon mustard together in a large bowl. Drain fusilli and vegetables and mix in. Cover and refrigerate, 1 to 8 hours. Sprinkle paprika on top before serving.