Some airways are class D for example IOM.
While you need an IR to cross the airway (except at the base where the airway is defined as a FL) it is not the controllers job to police qualifications. It is no different from entering IMC without an IR. So the controller will not ask; he assumes you are qualified. In theory if offered you would say unable to comply, or if not offered would not have asked in the first place. If the choice was between crossing or descending into IMC then I would declare a Pan and you would get the crossing I am sure.
You will in reality get the crossing at whatever level you request assuming there is no conflict - after all if you think about it, it really doesnt matter to the controller as the time you take to cross will be no different.
In reality if you clearly know what you are doing and behave yourself I cant imagine anyone is bothered if you cross at right angles for the few minutes you will be inside CAS but then that is only my opinion.
