I have enormous respect for the non-native English speakers on HN and their/your incredible mastery of the English language - it's truly astonishing how good nearly everyone is. But in this case my inner grad student needs to insist on the English meaning of the word. The etymologies do trace "cobblestone" and "cobbler" to a common root (though not definitively), but there doesn't seem to be any meaning of "cobbler" that refers to cobblestone makers. I don't know what the latter would be called - maybe cobblestone masons?
With the Shoe Cobblers it makes it clear it's talking about shoe manufacturers.