It would definitely get messy.
Snake Eyes raises a good point - what information was stated up front about international shipping? If neither of you discussed it, then I think this situation would probably fall into a gray area. If you did state that shipping would be at cost, the buyer is probably eligible for the PL.
Without knowing the particulars of the book, can you find another buyer without taking a loss? If I was in your spot AND could sell the book elsewhere, I'd tell the buyer that you're uncomfortable committing mail fraud and cancel the deal. As for putting the buyer on the PL, I'd be hesitant to do it. However, I'd probably never do business with them again either.