In my limited experience, most Zimbabwe elephant cow hunts are tuskless hunts, as least in the Parks areas. I have seen tusked cows listed as available in communal areas but do not know the details.

Edit: It was clear for my hunt that (a) it was for tuskless only, and (b) not exportable. I am surprised that whoever you booked through did not make that clear. Did you book directly with HHK?