If a President dies, then per Section 1 of the 25th Amendment, their Vice President becomes President. Not the Acting President; full-on President. It doesn't matter whether or not it's during a presidential transition (let alone two days before a President-elect's inauguration). And the swearing-in would be treated just like any other ascension to the Presidency, meaning the Chief Justice would conduct the swearing-in (unless, of course, it's an LBJ-type situation where the new President is on the other side of the country from the Chief Justice, in which case, a public officer ranging from a judge to a notary public can conduct the swearing-in).
This, except the swearing in is really just symbolic in this scenario. If the President dies, the Vice President becomes the president immediately, no oath of office required (probably). LBJ supposedly did the whole taking the oath on the plane thing because he was afraid AG Bobby Kennedy would find some loophole to screw him out of the presidency, so he wanted to make double-sure that he was really the president.
Yes & no. Yes, the VP does become President immediately upon the death of the preceding President, but no, the swearing-in isn't just symbolic. Per Article II, Section One, Clause 8, the VP-turned-President would be
required to take the oath before they're able to exercise or carry out any presidential powers or duties.
(And
according to Robert Caro, aka the world's leading LBJ expert, Bobby only influenced LBJ's swearing-in insomuch as LBJ demanded legal advice from him on how to take the oath of office. Personally, I've always interpreted it as LBJ trying to rub it in the distraught RFK's face that it was LBJ who was in charge now, but perhaps I've just re-watched
The Kennedys miniseries too many times for my own good lol)