With Martin’s setup that would be the result. You can see the background in any color you like while keeping the light spill of the HDRI you are using. The light path node set to camera ray is telling blender to use the B socket of the color mix only for viewing purposes, it’s not actually changing the result of the HDIR, it’s tricking Blender to change what you see, but not the actual light calculation. So you’ll be able to keep the blue tint while visualizing any background color you like.
