It looks like TX law for public lands (at least as it applies to this particular public land) is similar to other states. They consider public land hogs to be "small game" and as such you must use "small game" weapons and loads. In states like GA, the small game loads also include rimfire rifles,archery and muzzleloaders. I'm suspecting TX is the same. That presents a problem when the particular place you want to hunt also includes a "shotgun only" limitation. What you are left with is the only legal weapon happens to be insufficient for the job at hand. Sure, you can kill a hog with #4 shot (basically a squirrel load) but you need to be VERY close and shoot it behind the ear.
The other viable option you might have is archery. Many of the public lands that are "shotgun only" have an archery exception.