Combine cooked shredded chicken with salt, pepper, and 1 tablespoon melted butter from the Buffalo sauce in a large bowl.
Take about 2 tablespoons of the chicken mixture, flatten it, place one cube of mozzarella in the center, and fold chicken around to form a 3 to 4 inch stick. Press gently to seal.
Place sticks on a parchment-lined tray, refrigerate for 15 to 20 minutes, then freeze for 10 minutes to firm up.
Set up three shallow dishes: flour in one, beaten eggs in another, and panko combined with garlic powder and smoked paprika in the third.
Dredge each stick in flour, dip in eggs, coat with panko mixture, then repeat egg and panko coating for extra crispiness.
To fry, heat 2 inches of vegetable oil to 350°F and fry sticks in batches for 3 to 4 minutes until golden and cheese melts.
To bake, arrange sticks on parchment-lined sheet, spray lightly with oil, bake at 425°F for 12 to 15 minutes, flipping halfway.
Whisk together hot sauce, melted butter, honey, and optional cayenne. Toss hot cooked sticks in the Buffalo sauce to coat evenly.
Serve immediately garnished with chopped chives or parsley and ranch or blue-cheese dressing for dipping.