Zanchet, almost disappeared is Venetian, Zanchetta is typical of the Veneto and the low Friuli, Zanchetto, extremely rare is also Venetian, derive from dialect nicknames originated from physical defects (see Zanca), traces of these cognominizations we find In Verona at the beginning of 1500 when in an act of 1530 in Tarmassia (VR) We find a certain Paolo Zanchetta. Additions provided by Roberto Zambon in my opinion the surnames Zanco and Zanchet and the like of the Venetian area should derive from the word dialectal Thanco (with the interdental pronunciation type the English article) which means left-handed. Still today we use the man Thanca to indicate the left hand.
You may be interested
Verba Volant, Scripta Manent