Tom, if you're required to use a customs form (it is actually a form used by the US Department of Customs, not the USPS) for the mailing, then you must use the form. When you sign the form (it is a government document), you are saying that the information you wrote on the form is correct. If the information is incorrect, then you have falsified a government document (you know what that means). Also,if it is incorrect and Customs either here or the receiving country discover it, then the mailing can be confiscated. The customs form must be on the outside of the package. It is a declaration of what is inside, and you are acknowledging that any country (including the US) may open the package for inspection.
The buyer is asking you to do this for one reason only: to avoid paying taxes. The buyer is asking you to violate the law so that the buyer can violate the law.
If the buyer files a complaint of no delivery, your copy of the customs form receipt and the USPS cash register receipt is what PayPal will require as your proof of mailing. Remember, on international mailing, PayPal only needs to be shown that you properly mailed it here. You do not have to prove that it was received in the other country. We went through this with a buyer from another site who lived in Israel. Claimed he didn't receive the item (it was not philatelic). The funds were returned to him by the other site. The documentation was then provided to PayPal, and PayPal returned the money.
Mark has been clear on this issue in the past. A buyer cannot ask a seller to break the law.