Jesus some of the people in this thread.....
I feel sympathetic to the OP's concerns. But how in any way does the guy who reached his hand over 'deserve' to be bitten. He came round to inspect work done. He wasn't breaking and entering. He was coming, presumably, to make sure the work was satisfactory. Signs or no signs I don't think he deserves to lose his hand for that, as 1 of our high brow posters suggests.
Edit: as someone else above notes, if the dog is prone to bite purely at the sign of a strangers hand them I would suggest it is dangerous and needs securing. Heaven forbid some kid had kicked their football into the garden and came to retrieve it. Be ok if that kid go mauled?! Hypothetical of course.