I am saying that you will probably be able to buy one, but you will not be able to register it.

You can probably buy one and get someone in your hotel to register it, or a bar maid or someone. If they won't even sell you it then you need to find a Peruvian to go there at the same time. Mine was registered by my girlfriend.

You will be flying there presumably through LIM and there is a Claro shop there, a cursory google indicates there is a Movistar shop there too but I don't remember seeing it. Like I said, I found that Claro doesn't work too well in Cusco. Also Peruvian mobile networks are semi geographic so it will cost you more to use a Lima cellphone in Cusco

Sorry Peruvian mobile networks are a lamentable pile of crap, I really wish I had something more encouraging to share with you.