I use my 25 year old Cuisinart DLC-X, I shred a mix of Mozzarella, Provolone, White cheddar, and parmesan cheese.
I find that the Mozzarella can even bog down my big DLC-X. i dont know how well it would do in a salad shooter; howevr, if you freeze your mozzarella it will act like a hard cheese when beeing shredded and require less power to be shredded.
I have a hand held zylis parmesan cheese shredder and i do love it.