Stir together the cheeses, mustard, Worcestershire sauce, garlic powder and cayenne in a medium bowl; stir to combine. Transfer to a 4-cup ramekin (it will need to fit inside your air fryer). Pour the beer and milk over the cheese mixture in the ramekin and cover the ramekin with foil.
Carefully transfer the ramekin to the air fryer and air-fry at 400 degrees F for 10 minutes. Stir a few times, then re-cover with the foil and continue to cook, whisking every 5 minutes, until completely smooth, 10 to 15 more minutes. Remove from the air fryer and whisk to make sure the dip is smooth. Serve with pretzels.
