Unlike cabinet positions, I don’t think the VP needs the approval of Congress. It’s the President’s choice.
I was curious, so I looked it up. A presidential candidate is, of course, free to choose his own running mate. But it takes Congressional approval to replace a sitting VP.
What surprised me was that approval of both Houses of Congress is needed in that case. It’s not like with, say, a cabinet position. Only the Senate’s approval is needed there.
Senate confirms. Lookup Ford VP nomination.
Oops! And the House.
Yes it does per the 25th Amendment: "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."