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?

We don't know! We don't have any knowledge who is the real satoshi Nakamoto is and if he is still alive or not. We don't know why mr. Craig Wright is claiming that he is the real Satoshi Nakamoto, but the thing is what if he really knows who Satoshi Nakamoto is? And he already know that the real Satoshi Nakamoto doesn't have the plan on revealing himself so Mr. Craig Wright is claiming it in order to gain the popularity that he wants. What if that is the case?
I don't mean to be too dismissive about potentially valid explorations that might be raised, but these kinds of pie in the sky speculations regarding what might be potentially "valid" CSW motives are common tools for trolls and shills to place too much emphasis on what is highly unlikely rather than focusing on more plausible scenarios...
In this case, the more plausible scenario is that the CSW is a fucktwat scam artist that just makes shit up and throws spaghetti at the wall until something might stick, and in that regard, it does not matter hardly at all to speculate in a way that attempts to cause CSW to appear anything less than narcissistic and/or deluded in regards to what he knows or might know.