Incredible how Italian sanity works, apparently they don't even know if a part can be covered by them or not but anyway there would be a long time to wait for "reasons".
But if you pay 1300€ in a private clinic you can do it like a week after you request it with the same surgeon who would have done it in the hospital.
Took only 20 minutes, some pain when the numbness wears out but nothing bad and now just have to rest a bit and wait for the next test to verify that i'm actually "free".
Nice experience.