At least I haven't yet been able to imagine a context in which there is a clear semantic difference between "that that" and "which that". No hardware warnings, either. I've always been a bit troubled by the double-that, and I know that some spelling checkers object, but as far as I can recall none of them has ever recommended "which that" as a replacement.
The first valid hit I found on Ngram:
I only know that that slice of attention caused me to actually shape a personality around the tale.
And right below it:
He assured me that that was his destination, so I hopped in.
And as I grow up I would know that that is the person I am suppose to be with for the rest of my life!
In none of those cases is replacing with "which that" valid.
which that may occur as a accidental collocation ("the toy which that child holds is made of wood"), but for what you probably mean you want it the other way 'round: that which.
Your first that is a demonstrative pronoun and remains the same. Only the second is a relative pronoun which can be replaced (and in my opinion should be replaced) with which.
That which does not kill us makes us stronger.
"I know that that isn't the answer" wouldn't work with "which that": "I know which that isn't the answer".
From the answer to this question: How do you handle "that that"? The double "that" problem
We have the subordinating that (“I know that this is the answer.”) is doubled up with a demonstrative pronoun that (“That is not the answer.”) or an adjectival that (“That answer is not it.”).
Depending on the exact sentence you can often replace the subordinating that but not always with "which".