Oh you are being naughty aren't you?
"The right method of philosophy would be to say nothing except what can be said, that is to say the propositions of natural science."
Now forgive me if I'm wrong but I think he said
"Wovon man nicht sprechen kann, darüber muss man schweigen.“
Somehow the bit about the propositions of natural science in your quote seem to have magically appeared inside the quotation marks - your words not his!
Anyway I think the flaw in this logic is to believe that scientific 'fact' equates to absolute truth.
Clearly it doesn't - even the most certain science, mathematics relies on certain axioms, if you undermine any of these you bring down the house of cards as shown in non-euclidian geometry and Godel's incompleteness theorum etc.
However just because it does not represent 'absolute truth' does not make it meaningless
You can't say a motor car is just as useless as a horse and cart just because a car may get punctures occasionally.
Within the scientific method we use terms like 'proof' to have specific meanings rooted in statistics - the Higgs boson for example was proved at a 5.9 sigma level of certainty.
That is a long way from being meaningless - it is based in probability not words
Such probabilistic 'proof' is a feature of modern science that has become prevalent since Wittgenstein's time - he is essentially a critic of 19th century science.
Using him as a weapon to beat Science up with is not really anymore valid than using the Church's treatment of Gallileo as a weapon to beat them up with