Toss together carrot, cucumber, cheese and onions in small bowl.
pread 1 teaspoon dressing on each tortilla. Place 6 slices ham over each tortilla. Place lettuce leaf in center on ham. Spread one-third of the vegetable mixture (1/4 cup) down center, top to bottom, of each tortilla. Fold one side of tortilla over vegetable mixture and roll to wrap.
Serve immediately or wrap each in plastic wrap or foil for take-with sandwiches.