Do you think that Cry, The Beloved Country would have been different if it was written by a black author experiencing racism and pre-apartheid first-hand? How might Kumalo's character or perspective be different in the hands of a black writer?

This answer assumes that the type of work considered would also be fiction. One factor to consider in thinking about an author's race is that a writer is an individual as well as a member of a group. There are many black and white South African writers who have written critically about their country's political and social injustices under apartheid, and the differences among their perspectives are not neatly divisible along racial lines. However, each individual is going to be influenced by their own personal experience of race and discrimination when discussing the subject of apartheid.
Another important factor to consider is the time period—when the novel is set and the period when the author was actually writing. In Cry, the Beloved Country, Alan Paton presents many sympathetic and unsympathetic characters that are black and white alike. The character of Absalom Kumalo is not a bad person, but he makes bad choices. Arthur Jarvis, the white man he kills, has made good choices, especially in his efforts to help black South Africans.
However, a black author might handle the plot, the characters, and the events differently. For example, the plot might revolve around an incident in which a black protagonist is working toward ending apartheid and the killer might be a white man. Absalom's father, Stephen, reaches out to Arthur's father after his son kills Arthur.
Stephen seems to have been ignorant of the full extent of racially-based discrimination and injustice that was perpetrated against him, which does not always come across as realistic. A black writer might draw a character who is more fully aware and acts out of that knowledge: perhaps a clergyman more similar to Desmond Tutu.