Shimmering waters without reflection

I am not entirely sure I understand this correctly, perhaps you can describe it a little more. But generally, the glare from the water's surface can be reduced by using a circular polarizer filter in front of your lens. By turning the orientation of the circular filter, you can adjust how it filters out the glare.

The comments and other answer mostly focus on reflections of ambient light on the surface of the water, which can indeed be greatly reduced by a polarizing filter. However, you ask about reflections from the water fixtures. Those will be very hard to remove using only a filter. The reason is that the fixtures, which most likely are reflective chrome, reflect light in various angles and from various sources, and so some of the reflected rays will always be able to pass the polarizer.

I think you will need to look into setting up dedicated lighting (i.e. don't use ambient room light) and use black cloth to cover everything around your actual scene. Alternatively, use a dedicated tub that you only use for photography.