Preheat your oven to 425°F if baking the chicken, or heat a large skillet over medium-high heat.
Pat the chicken dry with paper towels. Drizzle with olive oil and coat with chili powder, smoked paprika, garlic powder, onion powder, cumin, oregano, salt, and pepper until evenly covered.
Bake the chicken for 18–22 minutes or cook in a skillet for about 5–6 minutes per side until the internal temperature reaches 165°F.
Transfer the cooked chicken to a cutting board and let it rest for 5 minutes before slicing into thin strips.
While the chicken rests, whisk together the Greek yogurt, mayonnaise, lime juice, chili powder, smoked paprika, garlic powder, cumin, hot sauce, and salt until smooth.
Warm the tortillas in a dry skillet or microwave for about 20 seconds.
Spread a spoonful of southwest sauce over each tortilla.
Layer with romaine lettuce, sliced chicken, black beans, corn, tomatoes, avocado, cheddar cheese, cilantro, and red onion.
Fold in the sides, roll tightly, and place seam-side down.
Toast each wrap in a skillet for 2–3 minutes per side until lightly golden and crispy.
Slice in half and serve with extra southwest sauce and fresh lime wedges.