No, there isn't. The Form 4473 was instituted after the GCA of 1968. At that time, there was no way to quickly verify the truth of the statements made on the form. So buyers filled out the form more or less "on the honor system," with the proviso that they could be prosecuted later for lying. In the meantime, they could get their gun. The Brady checks (with a 5-day waiting period) came in in 1993, and the instant checks (NICS) weren't fully implemented until 1998.
Now that we have NICS, with a robust database, we don't need the paper form. Everything could be done electronically. The paper form lives on, I think, as a convenience for the dealers.