Line cookie sheet with waxed paper; spray waxed paper with cooking spray. Wash and dry apples; remove stem and blossom ends. Insert craft stick into stem end of each apple.
In 2-quart saucepan, mix sugar, water and 1/4 cup of the corn syrup. Heat to boiling over medium-high heat. Cook about 8 minutes, without stirring, to 300°F on candy thermometer or until small amount of mixture dropped into cup of very cold water separates into hard, brittle threads. (Watch carefully so mixture does not burn.) Immediately remove from heat.
Working quickly, dip each apple in sugar mixture. Place on cookie sheet; let stand 4 minutes.
Meanwhile, in top of double boiler, mix remaining 3/4 cup corn syrup, the peanut butter and shortening. Cook over simmering water about 4 minutes, stirring constantly until smooth. Dip coated apples almost completely in peanut butter mixture; roll apples in chopped peanuts, using hands to help adhere if necessary. Return to cookie sheet; refrigerate 15 minutes or until set. Store covered at room temperature.