I suppose it depends on the meaning of "shall" in the second section of the 25th Amendment:
Would an acting president be violating the Constitution by simply refusing to nominate a vice president?
There is no Constitutional requirement to actually fill the position between elections, AFAIK. LBJ did not have a Vice President between JFK's assasination and January 20th, 1965 when The Hump was sworn in.
That was before the 25th amendment, which was enacted in 1967. LBJ could not appoint a Vice President (like others before him, Truman or Teddy as an example). Nixon was able to appoint Ford since Agnew resigned, because the amendment had been the law of the land in 1974, but not in 1963.
I think that the acting president could appoint a new Vice President, who would become president immediately after taking office. Acting president (or anything else, like acting governor) means, that the office itsself is vacant. The acting president is not holding the office, he or she only fullfills the duties of the post like signing bills into law. That's my personal interpretation.
Though it is a very intersting question, I suppose that matter had to be decided by the courts if we find ourselves in such a scenario. The difficulty to answer this is, that the line of succession existed before the 25th amendment, which allows the president to appoint a VP. Before 1967, this was not possible. Had LBJ died a few weeks into his term, House Speaker William McCormack would have become acting president until Jan. 20, 1965. However, such a case almost happend a few times (in 1868, when Andrew Johnson's impeachment failed by a single vote or Chester Arthur just died a few months after he left office; both times there was no Vice President). However (or ironically), the 25th amendment makes it less likely that any other person like the Vice President assumes the presidency.
