1. Heat corn syrup, sugar, butter, and 3/4 cup plus 2 tbsp. cream in a 3-qt. saucepan over medium-high heat until mixture reaches 275° on a candy thermometer*, about 15 minutes, stirring often with the thermometer or a wooden spoon once it starts to brown. While caramel boils, prepare the remaining ingredients (you'll need to have everything ready before beginning step 3).
2. Grease a baking sheet and set aside. Put nuts, chocolate chips, and candies on individual plates and set aside. Using a 1-in. melon baller, cut apples into balls (you should get 8 to 10 from each apple). Push thickest end of a twig into each apple ball through skin side to center. Set on paper towels to absorb moisture.
3. Remove caramel from heat when at 275° and pour in remaining 1/4 cup cream, stirring until very smooth (it will come together after about 1 minute) and being careful of any splattering caramel.
4. Dip apple balls into caramel, making sure caramel comes over edges of skin and letting excess drip off. Dip bottom of each ball into either nuts, chocolate chips, or candies, then set on the baking sheet to cool.
*You'll need an accurate candy thermometer. Check it by immersing in boiling water; it should read 212°. If it's a few degrees too high or low, cook the caramel to a corresponding few degrees more or less. If it's way off, get a new thermometer.
Make ahead: Chill until ready to serve, up to 3 hours ahead. Serve at room temperature.
Note: Nutritional analysis is per mini apple.