I would imagine it's a combination of both. Any son of a man like Vito would be hesitant about taking over for his father. His father was so loved and respected, was considered a great man by many. For any son to suddenly have to fill that role would be intimidating. Big shoes to fill.

And as much as this was "business and not personal", Sonny was still a son who loved his father, and who was frightened that his father would die. I would imagine that the hesitation was a little insecurity and a little bit of sadness and fear for his father's life.