Combine cucumber slices and vinegar in a medium bowl; let stand, stirring often.
. While cucumber stands, brush chicken with oil; sprinkle evenly with ginger, salt, and sesame seeds, pressing to adhere. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add chicken; cook 3 minutes on each side or until done. Remove from heat; keep warm.
. Place 1/2 cup cabbage and 1/2 cup cucumber slices on each wrap. Cut chicken into strips, and toss with Peanut Sauce. Arrange chicken over cucumber. Roll up; secure with wooden picks, if necessary.