Am I the only one who uses a food processor to "grate" - actually shred - large amounts of semi-hard cheeses.
Every food processor I have owned, since I got my first one decades ago, has had a shredding disc and it works fine for cheddar, fontina, swiss, jack, colby, &etc.
Just cut the cheese into a long piece that will fit in the tube, chill it in the freezer for at least half an hour to an hour if it is not real hard turn the motor on and gently push on the column of cheese.
I use the larger for these semi-hard cheeses and I use the smaller for hard cheese.