Heat a large skillet over medium-high heat. Cook and stir ground chicken in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease.
Melt butter in the skillet with the cooked chicken. Stir cayenne pepper sauce into the chicken mixture and remove from heat.
Squeeze as much moisture from the ricotta cheese using a cheese cloth or paper towels; put drained cheese in a large bowl. Add chicken mixture to the cheese and stir. Refrigerate until completely chilled, 3 to 4 hours.
Preheat oven to 375 degrees F (190 degrees C). Prepare a 13x9-inch baking dish with cooking spray.
Bring a large pot of lightly salted water to a boil. Cook pasta shells in the boiling water until cooked through but firm to the bite, about 10 minutes; drain. Rinse with cold water until no longer hot; drain.
Spoon chicken mixture into cooked pasta shells and arrange into the prepared baking dish. Sprinkle Cheddar-Monterey Jack cheese blend over the stuffed shells; season with salt and pepper.
Bake in preheated oven until the cheese is slightly melted and the stuffing is hot in the middle, 15 to 20 minutes.