Does cayenne pepper have antioxidants? Yes and broad variety at that: polyphenols, flavonoids, carotenoids, and vitamin C. However given that the latter, vitamin C, is easily destroyed by heat and light, very little (if any) remain in finished products such as cayenne powder or hot sauce.
Ranking between 30,000 to 50,000 SHU on the Scoville scale, it is not that spicy of a pepper. Then again, spiciness is quite subjective and tolerances vary greatly.
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010