I don't think any "swearing in" is required for an Acting President, the Vice President would just assume the duties of President.
In other words, despite of who you or I would like to see as President, there is nothing in the Constitution that dictates who Congress must pick to replace the disqualified President-elect.
This is not quite true. Section 4 of the XXth amendment states:
The Congress may by law provide for the case of the death of any of the persons from whom the House of Representatives may choose a President whenever the right of choice shall have devolved upon them, and for the case of the death of any of the persons from whom the Senate may choose a Vice President whenever the right of choice shall have devolved upon them.
That implies that the list of "persons from whom the House of Representatives may choose a President", is limited. So where is that limit to be found?
It's in the XIIth amendment:
from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President.
The XIIth also specifies *how* the House is to proceed.
in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice.
I'm afraid that, according to the 20th and 25th Amendments, and the Succession Act of 1947, in the event that the President-elect resigns or is removed from office, the vice-President-elect would become the President-elect and then be Inaugurated, assuming, of course, that the vice-President-elect does not resign or is not also removed.
However, one of the questions that SCOTUS ought to answer is whether this entire election was legitimate. I think that, if Obama is disqualified on the basis of what his vault birth certificate says, then that's when the entire Democratic Party takes a torpedo amidships.