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.
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.