When I think of cleaning stonework, the first thing that comes to mind for me is to use a product that is known to be safe and common to the water already like bleach or muriatic acid. You can experiment with either one separately, combined with water in diluted mixtures. See which one gives the best results. You might need a small brush to agitate the cracks and crevasses. Inevitably some residue may fall into the water, but some may oxidize in place. Maybe others will have some more ideas. Very nice pool though.