The majority of Fred's post-78 recordings were film soundtracks. Not to downplay the quality of the soundtracks, but there are some noteable exceptions you may wish to investigate:
The Fred Astaire Story (December 1952)
Astaire sings jazz? Practically every song associated with Fred up to that point, accompanied by the extraordinarily talented Oscar Peterson (reccommended by Fred jr) and recorded live in the studio. The CD version omits two 'dance' numbers, where Fred does not sing.
Fred Astaire Sings (1955)
A studio album of (mainly) Astaire classics, conducted by
Astairable Fred
The CD version contains a live medley from each of the three 'Evening With Fred Astaire' TV programmes (worth having if for no other reason than the comic rendition of Miss Otis Regrets by Fred and Barry Chase), as well as what appears to be a collection of singles from the 1950's-- unfortunately we are given no information other than the names of the conductors.
All are still available in the US, and are well worth the price of admission.