Preheat a grill or skillet over medium heat. Season the chicken breasts with garlic powder, onion powder, ground ginger, salt, and pepper.
Cook the chicken for about 6-7 minutes on each side, or until fully cooked and no longer pink in the center. Remove from heat and let it rest for 5 minutes before slicing into thin strips.
In a small bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, lime juice, and sriracha (if using) until smooth and creamy. Adjust the consistency with a little water if needed.
Lay out the whole wheat tortillas on a clean surface. Spread a generous amount of the creamy peanut sauce on each tortilla.
Evenly distribute the sliced chicken, shredded carrots, red bell pepper, cucumber, and cilantro leaves on top of the sauce.
Roll up each tortilla tightly, tucking in the sides as you go to create a wrap. Slice in half diagonally to serve.