Heat oven to 350 degrees F. Place nuts, each kind separate, on a rimmed baking sheet. Bake, stirring once or twice, 8-10 minutes until lightly toasted. Let cool.
In a food processor, pulse one kind of nut at a time, until just finely chopped (don't overprocess). Place in separate bowls.
Remove blade; wipe processor bowl clean. Add cheeses; process until blended and smooth. Scrape into a medium bowl.
Line rimmed baking sheet with wax paper. Gently fold grapes into cheese mixture. Remove 1 coated grape at a time with a spoon, then push grape gently into one of the bowls of chopped nuts. Shake bowl to turn grape until coated. Place on lined baking sheet.
To serve: Arrange grapes on a leaf-lined plate to resemble a bunch of grapes.