I'm picturing a simple scenario: 2 black holes about to merge and they are receding away from us at constant speed. (I like to negate the rate of expansion of space and assume universe is perfectly flat for now, don't argue with me I'll bite)
Back to my story, I think my hypothetical detector should observe that the wavelength of hawking radiation becoming redder(longer with you will). How about the gravitational wave? I mean how do we know that the gravitational wave is red shifted, in this case the accompanying light cannot testify also there is no way to directly measure it.(don't confuse with gravitational red shift like google or bing usually do, believe me it's utterly annoying to see millions of similar result)
Complimentary question: is there any way to test if the energy of a gravitational wave is quantized?