Step 1Place empty ice-pop molds in the freezer to chill. Dice 2 pounds of the cucumber into 1-inch pieces; do not remove the skins. Place the pieces in a food processor or blender and puree until smooth. Strain into a medium bowl through a fine mesh strainer, pushing out the juice with some of the pulp. You should have 2 1/2 cups juice and pulp. Set aside.
Step 2Peel the remaining half-cucumber and cut it into half-inch-by-one-eighth-inch pieces. Set aside in a small bowl.
Step 3Add the lime juice, sugar and crushed chile pepper to a small sauce pan. Cook over medium heat, stirring occasionally, until the sugar is dissolved. Remove the syrup from the heat and cool slightly.
Step 4In a small bowl, combine the chile powders. Strain the cooled syrup into the bowl with the cucumber juice, discarding the crushed pepper. Stir in the salt and one-fourth teaspoon of the combined chile powders.
Step 5Pour some of the mixture into each mold, leaving about a half-inch of space at the top. Stir several pieces of cucumber into each mold. Place lid on the molds and fit with the wooden stick. Place the molds in the freezer and freeze until solid, 2 to 4 hours.
Step 6Remove the molds from the freezer and run them briefly under warm water to loosen the paletas. Gently pull them from the molds and sprinkle the tops lightly with the remaining chile powder mixture to taste, if desired. Wrap the paletas in plastic wrap and return them to the freezer if not serving immediately. They will keep 1 to 2 weeks in the freezer.