The premise of the question is flawed assuming that damage must occur in order to feel pain. Our nervous network allows us to sense pain as a warning, true, but that does not mean that it is exclusively triggered by damage. A common examples is how spicy foods trick our senses into believing we are being burned (as if by heat) when actually no damage is being done.
A Kryptonian's nervous network arises from a planet without invulnerability so it would still be calibrated to sensation on those levels, irrespective of any invulnerability. He would still feel pressure to the same degree, heat, and the like. However, after developing a lifetime of experience his personal pain tolerance would adapt to his invulnerability. So electrical shock, something that he ultimately knows won't harm him, simply "tickles".
You can see this scaling of psychological tolerance in the taste for spicy foods or athletic pain tolerance. The one acclimated to spicy food can eat something four alarm with nary a bead of sweat, while objectively no-less sensitive to the spice... while someone unaccustomed finds themselves tearing, gagging, and reaching for relief. Likewise, an athlete may enjoy feeling the burn while the couch potato whines and groans just getting up.
In all these cases, there is no actual physical or permanent harm and the objective sensation is the same, but the subjective experience is different. This is how Superman can feel a kiss brush across his lips but also laugh at a lightning bolt.