In a bowl, toss coleslaw mix, carrots, cider vinegar and 2 tablespoons of the dressing until combined.
Spread each wrap with 1 tablespoon of the remaining dressing. Line each wrap with a piece of lettuce. Place 2 slices of turkey or pastrami on top of dressing in center. Place 2 slices of cheese on top of turkey. Top with about 1/3 cup of the coleslaw. Roll up burrito-style, tucking in sides.