Preheat oven to 375 degrees F. Lightly coat a cookie sheet with cooking oil or nonstick cooking spray; set aside. Combine the papayas, lime peel, lime juice, and honey in a medium bowl; set aside. Spray one sheet of phyllo with cooking oil or nonstick cooking spray. Sprinkle with about 1 tablespoon of the crushed cookies. Place a second sheet of phyllo on top of first sheet. Repeat coating and sprinkling with remaining sheets of phyllo. Sprinkle the remaining crushed cookies atop the last sheet of phyllo.
Spoon papaya mixture onto the phyllo stack, leaving a 2-inch border on all sides. Fold the long edges of the phyllo stack up over filling, then fold in the short sides. Roll up from one long side into a cylinder. Carefully lift cylinder and place it, seam side down, onto prepared cookie sheet. Lightly coat the top of the strudel with cooking oil or nonstick cooking spray. Score into 10 slices, cutting only through the top layer of phyllo, about 1/8 inch deep.
Bake in preheated oven for 25 to 30 minutes or until golden brown. Sprinkle with powdered sugar before serving. Serve warm. Makes 10 servings.