When using Light as if Static the lighting will be baked for all objects, including those you choose to switch out. There isn’t a way around this unless you unchecked the option for cast shadow, but then you wouldn’t have any shadows at all.
As a workaround, you could explore having a low-intensity point light in place to help cast some softer shadows. You would set this to be dynamic so that there are no baked shadows and it will affect the objects that are being switched out.