I would advise against it.
If it's done well no one will probably be the wiser but it's a slippery slope. Once you get into that mode of amending documents to appease customers it becomes easier than actually doing the work for future requests. You might also become 'the guy' around the office who can get you the "documentation" you need trapping yourself in that role of forfeitures where you'll eventually get caught in a lie or have to disappoint people by telling them "no I won't/can't do that".
But that the answer you knew you would get. Am I right?
It's not worth the worry but if that's the route you take, I would get the ball rolling on getting a legit version free of adulteration, reissue the COA to the customer and try to avoid making it a habit.
All theoretical btw and from the experience of SWIM.