We have had the odd feisty wether, but I agree, it does sound as if there's more testosterone in your boy's bloodstream than you would expect of a wether

Have a good look at the shelter to see exactly where he's beating it up. Is there loose tin which makes a louder noise than wood? Is it made of metal or wood? Is he whacking it on a corner post or the walls? is he whacking it inside or out?
We have had tups which beat up their shelters and go for the weakest point, which is usually the internal or external walls. We wrap the shelters in sheep mesh, so there's not that satisfying crack, just a bounce back, and the shelter stays in one piece. If he's hitting a corner post, you could bash in a stob a few inches out from the corner, which would block his access. You could move the shelter further from your bedroom, so you can't hear him. You could put a strainer post somewhere further away so he will smack his head into that and leave the shelter alone. All he wants is the satisfaction of hitting his head off something satisfyingly hard, so by providing him with an alternative, you might save the shelter.
If he is a rig, and you also have ewes, then he isn't appropriate to run with them, unless you want lambs
