Appointment of a VP does not require Congressional or SC approval. It is an arbitrary act by the president and can be accomplished in minutes. It requires notice of the individual and a judge to swear the candidate into office.
It is conceivable this can be done and held in abeyance pending necessity.
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.