Well, here's what Wikipedia says, it seems he was "Zuan Chabotto", and not Giovanni Cabotto, as you said.
Quote:
Only one set of documents has been found bearing his signature. These are Venetian testamentary documents of 1484, on which he signed as "Zuan Chabotto", "Zuan" being a form of "John" typical to Venice.[3] That he continued to use this form in England, at least among Italians, is supported by two letters referring to him that were written by others in London in 1497.
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http://en.wikipedia.org/wiki/John_Cabot
And - I have heard about the destroyed documents, it's absolutely incredible that someone would do that unless she was in doubt about some of her facts and thought they might be misinterpreted.