Wash and dry the cucumbers. Using a vegetable peeler or mandoline slicer, slice the cucumbers lengthwise into thin, even strips about 1/8 inch thick.
In a medium bowl, combine the shredded cooked chicken, Greek yogurt, mayonnaise, Dijon mustard, chopped celery, chopped red onion, fresh dill, fresh parsley, lemon juice, and garlic powder.
Mix the chicken salad ingredients thoroughly until well combined. Season with salt and black pepper to taste.
Lay out a cucumber slice flat on a clean surface. Place about 2 tablespoons of the chicken salad at one end of the cucumber slice.
Carefully roll the cucumber slice around the chicken salad filling to form a tight roll.
Repeat the rolling process with the remaining cucumber slices and chicken salad filling.
Arrange the cucumber rolls on a serving platter and serve immediately or refrigerate for up to 2 hours before serving.