Just an idea. If Craig Wright is NOT Satoshi Nakamoto, he would definitely risk the real Satoshi come up with a proof, that Craig is not SN. Is it possible, that CW explicitly knows about the death of the person behind SN, so he can make his claims without backing them up with a proof?

It's not only possible. It's reality.
On 26 August 2019, a US Federal Court ruled that Satoshi Nakamoto is the partnership of Dave Kleiman and Craig Wright. And Dave Klieman, as we all know, is dead.
https://gizmodo.com/the-strange-life-and-death-of-dave-kleiman-a-computer-1747092460"Dave Kleiman was found dead in his home. According to reports provided by the Palm Beach County Medical Examiner Office, the scene of Kleiman’s death was gruesome. His body was decomposing, there were wheelchair tracks of blood and fecal matter, open bottles of alcohol, and a loaded handgun next to him. A bullet hole in his mattress would seem to suggest suicide or foul play, but no ammunition casings were found, meaning he might have fired his gun and cleaned up sometime before dying."
Most likely the result of a professional hit to keep him quiet about his involvement with Bitcoin.
Interesting, that guy is always on step ahead...