I'm no expert (and sometimes it shows) but my $$$ says that the noise is the result of expansion. As the piping gets hot, the metal expands and creates a popping noise. If possible, buy some pipe insulation and cover whatever pipe you can, including under the sink. This will help keep the pipe warm and improve the speed at which the water warms up, hence, less clicking.
I know you are saying that all the pipes are unexposed but there has to be some in the basement (or wherever) where you can insulate. Once the pipe enters the wall, you can buy 'spacers' to shore up the pipe. And lastly, if the pipes run up an outside wall (which is just bad plumbing in a general sense) you have to consider your options to insulate the pipe. I'll be listening to what others have to say because, as I said, I'm no expert and the solution(s) interests me too. My best to ya and hope this is 'some help'.