Is it possible to make kataifi dough (by yourself or starting from filo dough)?
I am afraid that it is quite hard to prepare it yourself. And you don't start from phylo dough. 

Kataifi is not shredded, it is spun. You need a hot metal wheel for that. It is made from a batter which is thrown on the wheel, and because the wheel is spun, it bakes on the wheel in threads. You need not only the instruments (this wheel), but also quite a bit of experience to throw it in even threads. Kataifi makers are a popular attraction on middle-eastern markets. If you can't visit one, you have to visit an ethnic grocery store to buy the prepared kataifi noodles.