I'm not sure I understand the question.
The shipping cost would be passed to the person purchasing and not involve you.
I think for something like this, using the USPS Flat Rate shipping method would be best. the person giving the item away would have to determine what USPS Flat rate Box size the item would ship in, when they add the item to the database, they include shipping box size, and/or price. For example 5.60 for a small flat rate box. 12.35 for a medium flat rate box etc.