Make the dressing: In a small bowl, whisk together mayonnaise, ketchup, pickle relish, horseradish, lemon juice, and Worcestershire. Season with salt and pepper.
Arrange half the pickle chips on a platter. Top with sliced corned beef, Swiss, sauerkraut, and drizzle with dressing. Close the bites with remaining half of pickles and a toothpick.
