Mix the sauce. In a small bowl, stir together the sour cream or Greek yogurt, mayonnaise, lime juice, chili powder, cumin, garlic powder, salt, and pepper. Taste it and adjust the seasoning if needed.
Prepare the filling. In a large bowl, combine the chicken, black beans, corn, tomatoes, red onion, cilantro, and a few spoonfuls of the sauce. Mix gently so everything gets coated without turning mushy.
Warm the tortillas. Heat the tortillas in a dry skillet for a few seconds per side, or microwave them briefly until soft.
Warm tortillas roll more easily and hold together better.
Assemble the wraps. Lay each tortilla flat and add a layer of lettuce, then spoon the chicken mixture down the center. Top with cheese and avocado, and drizzle on more sauce if you like extra creaminess.
Roll them up. Fold in the sides, then roll tightly from the bottom to form a wrap. If needed, secure each one with parchment paper or a toothpick.
Serve right away. Slice the wraps in half for easier eating and serve with extra lime wedges, salsa, or chips on the side.
They taste best when everything is fresh and the tortillas are still soft.