I looked it up. It turns out we were both wrong. You thought a VP nominee didn’t need confirmation. I thought only the Senate had to confirm.
The 25th Amendment, Section 2: Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.
Yes, if for any reason Mike Pence became President before Jan. 20, 2021, he could nominate a new Vice President, but the House could refuse to confirm his pick and then the office would remain vacant.