Whisk the reduced-fat peanut butter, reduced-sodium soy sauce, lime juice, rice vinegar, honey, toasted sesame oil, garlic, ginger, and crushed red pepper flakes in a bowl. Gradually whisk in the warm water until the mixture becomes smooth and spreadable, adding a little more water if needed.

Season the thin chicken strips evenly with salt and black pepper. Keeping the pieces thin helps them cook quickly and remain tender.

Heat the canola or vegetable oil in a large nonstick skillet over medium-high heat. Cook the chicken for approximately 4 to 5 minutes per side, or until browned and the thickest pieces reach 165°F/74°C.

Remove the skillet from the heat and let the cooked chicken rest for 2 to 3 minutes. Slice or chop it into bite-size pieces after resting so the juices have a moment to settle.

Warm the tortillas briefly in a dry skillet or microwave. The tortillas should be flexible but not crisp, which makes folding and rolling easier.

Spread approximately 2 tablespoons of peanut sauce over each tortilla. Add the cabbage or lettuce, carrot, cucumber, green onion, cilantro, and cooked chicken in an even line across the lower-middle portion of each tortilla.

Fold in the sides of each tortilla, then roll it tightly from the bottom upward. Slice the wraps in half if desired and serve with any remaining peanut sauce.