Slice the chicken breasts into thin strips and place them into a mixing bowl. Add olive oil, Cajun seasoning, garlic powder, smoked paprika, salt, and black pepper. Mix well until all the chicken pieces are evenly coated in seasoning. Let the chicken rest for 10 minutes for deeper flavor.
Heat a large skillet over medium-high heat. Add the seasoned chicken in a single layer and cook for 4 to 5 minutes without stirring too much so the chicken develops golden brown edges.
Flip the chicken pieces and cook for another 3 to 4 minutes until fully cooked and lightly charred. Remove the chicken from the skillet and let it rest for a few minutes to keep the juices inside.
In a small bowl, mix mayonnaise, hot sauce, lemon juice, garlic powder, and Cajun seasoning until smooth and creamy. Taste and adjust spice if needed.
Wash and dry the lettuce, dice the tomatoes, and thinly slice the onions. Warm the tortillas slightly so they become soft and flexible for rolling.
Lay the tortillas flat on a clean surface. Spread the creamy Cajun sauce across the center of each tortilla.
Add shredded lettuce, cooked Cajun chicken, shredded cheese, diced tomatoes, and sliced onions on top of the sauce. Do not overfill the tortillas.
Fold the sides inward and tightly roll each tortilla into a wrap while keeping the filling tucked inside.
Heat a clean skillet over medium heat. Place the wraps seam-side down and toast for 1 to 2 minutes per side until crispy and golden brown.
Transfer the wraps onto a cutting board and let them cool slightly before slicing in half. Serve warm with fries, salad, or dipping sauce.