Food with a wet batter works great in an air fryer with a baking sheet. Using parchment paper will make it easier to remove.
The air frier hush puppies will be easier to remove from the basket if you use it (no matter how well-oiled the basket is).
Avoid placing wet batter straight on the bottom of the air fryer basket. If you prefer, you can use aluminum foil, it works in the same way.