Choose squash that are uniform in shape so they will cook evenly. The best kind for this recipe are long, straight, and not too skinny.
Preheat oven to 375°F. Spread cornbread in an even layer on one end of a baking sheet. Cut zucchini in half lengthwise. Using a serrated tomato corer or melon baller, scoop out zucchini pulp to equal 3 cups pulp, leaving a 1/2-inch shell intact. Coarsely chop 1 1/2 cups of pulp; reserve remaining pulp for another use. Brush zucchini shells with 2 tablespoons of the canola oil. Place zucchini shells on baking sheet with cornbread, and sprinkle with 1/4 teaspoon of the salt. Bake zucchini and cornbread at 375°F until cornbread is lightly browned, 8 to 10 minutes. Reduce oven temperature to 350°F.
Heat remaining 1 tablespoon oil in a large skillet over medium-high. Add ground chicken to skillet; cook, stirring to crumble, until browned, 5 to 6 minutes. Add onion, garlic, paprika, pepper, reserved 1 1/2 cups zucchini pulp, and remaining 3/4 teaspoon salt to skillet; cook, stirring occasionally, until onion is tender, about 3 minutes. Transfer mixture to a large bowl, and stir in cornbread, white Cheddar cheese, corn, and parsley. Divide chicken mixture evenly among zucchini shells. Place shells on a baking sheet.
Bake stuffed zucchini at 350°F until filling is lightly browned and zucchini is tender, 25 minutes.