Preheat the air fryer to 400°F for 3 minutes while you prepare the shrimp.
Pat shrimp very dry with paper towels and place in a medium bowl.
Mix oil, lime juice, lime zest, chili powder, smoked paprika, minced garlic, salt, and pepper in a small bowl and pour over shrimp; toss to coat and let sit 10–15 minutes maximum.
Arrange shrimp in a single layer in the air fryer basket with minimal overlap; work in batches if necessary.
Cook at 400°F for 4 minutes, shake or flip shrimp, then cook an additional 3–4 minutes until edges are slightly charred and shrimp are opaque and springy.
Transfer shrimp to a platter, brush with any reserved marinade (not the raw used marinade), sprinkle chopped cilantro and extra lime zest, and serve immediately with lime wedges.