My recollection is that the presidential succession law states somewhere in the boilerplate that an officeholder ineligible to succeed to the Presidency (i.e. not a native-born citizen or younger than 35) would indeed be skipped over for the next in line.
You are correct - here is the relevant text of the Presidential Succession Act of 1947:
(1) If, by reason of death, resignation, removal from office, inability, or failure to qualify, there is no President pro tempore to act as President under subsection (b) of this section, then the officer of the United States who is highest on the following list, and who is not under disability to discharge the powers and duties of the office of President