Preheat the air fryer to 400°F for 3 minutes. Lightly spray the basket with nonstick cooking spray.
Arrange the frozen dino nuggets in a single layer in the air fryer basket, making sure none of them overlap. Depending on the size of your air fryer, you may need to cook them in batches.
Air fry at 400°F for 8 to 10 minutes, flipping the nuggets halfway through cooking. They are done when the outside is golden brown and crispy and the internal temperature reaches 165°F.
While the nuggets cook, make the dipping sauce. In a small bowl, whisk together the mayonnaise, ketchup, yellow mustard, pickle juice, garlic powder, and smoked paprika until smooth and creamy.
Remove the nuggets from the air fryer and let them cool for 1 to 2 minutes so they firm up and are safe to eat. Serve immediately with the dipping sauce on the side.