If Putin loses an arm, all of his doppelgängers will need to lose an arm too. Otherwise they’ll be immediately identified as doppelgängers.
It’s a pretty well known thing that Putin frequently uses lookalikes for public appearances. It’s apparently an old habit from when he was a KGB agent. So if someone snipes him from a rooftop, it’s probably not even him; He can claim to have miraculously survived the shooting, then carry on as if nothing happened.