Season chicken strips with chili powder, cumin, paprika, garlic powder, onion powder, and salt. Heat 1 tbsp oil in a large nonstick skillet over medium-high heat, add chicken in one layer, and cook 3 minutes per side until seared and cooked through. Transfer to a plate and wipe the pan.

Warm tostada shells in the microwave for 30 seconds. Warm flour tortillas one at a time for 15 to 20 seconds until pliable.

For each wrap, spread 2 tbsp nacho cheese in the center of a tortilla, top with one-quarter of the chicken, place a tostada shell on top, spread 2 tbsp sour cream over the tostada, then add lettuce, tomato, and shredded cheese.

Fold the tortilla edges up in overlapping pleats to fully enclose the filling, pressing gently so the folds hold. Place seam side down.

Wipe the skillet, add remaining 1 tbsp oil, and heat over medium. Cook each wrap seam side down for 3 to 4 minutes until golden, flip, and cook another 3 to 4 minutes until crisp.

Let the wrap rest 1 minute, then slice in half diagonally and serve immediately.