What pre Rock and Roll performer has had most recent hit?

Interesting anomaly, but Davis’s version of “Hey There” did get an official chart position on Billboard (#16). So he can’t really work. “Candy Man” was in fact his first #1.

For B, you almost answered your own question!

Perry Como, who had quite a few pre-1955 #1 hits, made it to #10 with “It’s Impossible” in 1971.

And for C, I believe it’s the aforementioned Frank Sinatra, for “Somethin’ Stupid” with Nancy in 1967.
So, in summary:

A) Nat ‘King’ Cole, “Unforgettable” (#14, 1991)

B) Perry Como, “It’s Impossible” (#10, 1971)

C) Frank Sinatra, “Somethin’ Stupid” (#1, 1967)
In the case of A and C, IMHO the presence of the artist’s name on the record label is enough for me, regardless of any accompanying “and”'s or “with”'s.