[sciurius]

Whether a key is theoretical or not does not really matter. Transposition is a step-wise process. One step up from D gives D# in Sharp mode, and Eb in Flat mode.
Transposition is only effective for ChordPro songs and these do not have key signatures, just keys. Often just chords.
Actually, as I wrote earlier, having a key property for a song is misleading because the song can have multiple keys. The Transposition dialog only deals with the last or only key, often based on the first chord. So it would be more appropriate to say that the Transpose dialog shows how the first chord of the song changes, and a chord change from D to D# is quite normal.
But this is nitpicking, not worth spending much energy on. I just think that the Transposition dialog should allow all steps.