Parmesan does well with butterfat below 2.5%. If you skim off all the cream, the milk should be somewhere around 2%, so you should be fine.
I don't know if the milk used to make parmesan in Parma is tested beforehand, but before they did testing, they just skimmed off the cream and used the skimmed milk. So just do that or use a mechanical separator and you should be fine.