You can use the visibility overrides, put an HDRI into the Reflection override. That way it shows up in the reflections of the windows (and any other reflections that would normally reflect that sky), but does not replace or add to the lighting, nor change the direct view of the sky.
If the rooms are regularly spaced, I'd suggest using an array, or a scatter using the regular repeats rather than randomization as the quick way to place a light in every room.