I am not a vocalist, but an instrumentalist.
When I want to transpose something up or down a half step, this takes considerable work: different hand/chord shapes on the piano, completely different fingerings on a brass or woodwind instrument, etc.
I have always assumed that transposition for vocalists is a relatively simple exercise, and that the only consideration that comes into play is range: transposing something up or down could make the higher or lower notes more difficult, but that's pretty much it.
Am I correct here, or are there other hidden difficulties for vocalists when they transpose?