I sent him to the depths of Hell, with the rest of the Institute. I watched the real Shaun die, I know the kid is fake, and I saw him before he got reprogrammed. Even one of the people in the Institute (I think Janet Thompson) said he would never grow up. So he and everyone around him would know he's a synth sooner or later, even if I wanted to raise him as a real son. Which I don't. I'd prefer to make peace with my real son's death than replace him with a robot.
If you still love him, I guess that's a good reason not to hang around the airship for too long. You'll probably have to build your own glorious house or settlement.