Preheat the oven to 350 degrees F. Slice the chicken into about 24 chunks. Slice each chunk in half hamburger style.
Slice the ham and Swiss cheese into squares that are about the same size as the chicken chunks. Sandwich a piece of ham and a piece of Swiss cheese between each pair of the chicken chunks and secure with a toothpick.
In a bowl or shallow pie dish combine the flour, salt, and pepper. In another bowl, beat the egg and water. Place the breadcrumbs into a third bowl.
Roll the chicken chunks first in the flour mixture, then dip in the egg mixture and then roll in the breadcrumbs until evenly coated. Place onto a greased baking sheet. You can leave the toothpicks in for now.
Lightly spray the tops of the nuggets with cooking spray and place into the oven and bake for 10 minutes. Then, remove the toothpicks, flip the nuggets and bake for 10 minutes more or until fully cooked (the internal temperature has reached 165 degrees F).
If you would prefer to deep-fry them instead of baking: Heat oil in a deep-fryer to 375 degrees F. Cook the chicken nuggets in batches until golden brown and fully cooked (the internal temperature has reached 165 degrees F.). Drain on paper towels. Remove the toothpicks before serving.