I use a food processor, but I don't shred them. I use the steel knife. Cut the peeled spuds and onions into chunks, then process with on-off pulses until most of the mixture resembles something like oatmeal. There may still be a few large chunks. Remove them, dump out the rest and try again.
This process gets you more or less the consistency you'd get grating on the finest side of a box grater, sans shreds of fingernail, bits of skin and drops of blood. (Yes, I know, the blood makes it taste better....)
Here's my family's recipe. I make these fairly thin.
Potato latkes
6 medium potatoes
1 small onion
1 egg, slightly beaten
3 tablespoons flour or matzo cake meal
1 teaspoon salt
1/4 teaspoon pepper
1/2 teaspoon baking powder
Peanut oil for frying
Peel the potatoes and onion and grate on the finest side of a box grater into a bowl. (To grate in a food processor, cut the potatoes and onion into chunks and process in small batches. Place in the bowl fitted with the steel blade, and process using on-off pulses, until the mixture is the right consistency.) Stir together. The mixture should resemble oatmeal or chunky applesauce.
Let stand 10 minutes so the liquid rises to the top. Pour off the liquid. Stir in the eggs. Add the flour, salt, pepper and baking powder.
Heat 1/4 inch of oil in a large skillet until very hot. Drop the potato mixture by spoonfuls into the oil. Don't crowd them. Flatten slightly with a spoon or spatula and brown on both sides. Drain on paper towels. Serve immediately. 6 servings.