To me, the problem is requiring you to organize the shipping yourself. Does this mean that you would need to hire someone local to go to the hotel and put the thing in suitable packaging rather than having some hotel staff member take care of such details? People leave stuff behind all the time in hotel rooms and the hotel should have a process to efficiently sent the items, although it's not unreasonable to expect the guest to pay FedEx or whatever fees, ideally using the hotel's account with a good discount attached.