Bake the Tater Tots as the label directs; let cool slightly.
Spread about 1/2 teaspoon mustard on 1 slice of ham, then sprinkle with 1 heaping teaspoon finely chopped dill pickle. Top with a Swiss cheese slice and cut lengthwise into 3/4-inch-wide strips. Wrap each Tater Tot in a ham-and-cheese strip and secure with a toothpick.
Position a rack 6 inches from the broiler; preheat the broiler. Coat a baking sheet with cooking spray. Transfer the wrapped Tater Tots to the prepared baking sheet and broil until the ham starts crisping around the edges and the cheese melts, 2 to 3 minutes.