If one were to fasten a sling to a pistol and carry it by placing the sling over one's shoulder, I don't see why that should be considered any different from placing a rifle sling over one's shoulder. Certainly I could understand how carrying a pistol in a holster might be considered "wearing" in a way that a slung rifle would not, but my understanding is that the rules in Texas related to possession of pistols without regard for their being particularly attached to one's person.
I see your logic, but the legislature has not included long guns on its prohibited list.