I saw a video a couple years ago where the guy was just taking the shoulders and cutting back straps out and not gutting. He didn't even skin, just cut them off and threw them in a brine.
I've seen that done, but they did skin it. Skin, take front and hind quarters and backstrap, and discard the rest. No mess. (or, very little!) And, all you really lose that might be worth saving are the tenderloins.