> Both C#m and Db can be played on piano using only the black keys (skipping the 3rd note of the scale)

For the major scale, there are 7 notes in the scale and only 5 black keys; you also need to skip ti, the 7th note.

For the minor scale ("C#m"), it's worse; only four of the five black keys are part of that scale.

And I would have thought that something intended to be played only on the black keys would be described as using a pentatonic scale anyway?

As a belated followup, I should observe that if you're playing "in C sharp minor" on the black keys, you're skipping notes 3, 6, and 7 of the scale... and those are the only notes that differ between a minor scale and a major scale, making the "minor" designation completely meaningless.