Add shredded chicken, mayonnaise, lemon juice, garlic powder, paprika, salt, and black pepper to a large mixing bowl. Stir until the chicken is evenly coated in the creamy mixture.
Wash and dry the lettuce, cucumbers, and tomatoes well. Shred the lettuce, slice the cucumbers thinly, and dice the tomatoes into small pieces.
Heat a dry skillet over medium heat. Warm each tortilla for about 15 to 20 seconds per side until soft and flexible.
Place one tortilla on a flat surface. Add shredded lettuce, cucumbers, tomatoes, cheddar cheese, and a generous spoonful of chicken filling in the center of the tortilla.
Fold the sides inward and roll the tortilla tightly from the bottom upward to create a secure wrap. Repeat with the remaining tortillas.
Heat butter or oil in a skillet over medium heat. Place the wraps seam-side down and toast for 2 to 3 minutes per side until golden brown and crispy.
Remove the wraps from the skillet and let them rest for 1 minute before slicing diagonally in half.
Serve warm with fries, dips, or salad.