I realize that the OP asked about TX, and each state will likely have different laws on the subject. Always check with the local powers that be if you want to make sure you are legal.
However, NY law may provide an insight into the original question.
In NY, you need a permit to posses, use, carry, or even touch a handgun.
However, certain blackpowder handguns are considered antiques (even replicas) and can be purchased and owned without any type of permit. So far, this seems to be similar the OPs understanding.
If you read further into it, you will find that as soon as you posses the "means to load" that blackpowder handgun then you now posses a "weapon" which requires a license and comes under all the restrictions of a "modern" handgun.
Beyond the simple possession/carry restrictions, there are also other legal considerations. If it looks like a gun and you carry it around or "brandish" it, you are likely to run afoul of the police, especially if you do not have a carry permit.
Again, local laws vary. But it is usually safe to figure that there are virtually no loopholes when it comes to carrying weapon.