What a coincidence. I recently stumbled upon a video of a young sort of guy in Arizona by the name of Kairo Seijuro who seems to have attained a high degree of skill in classical kenjutsu. He was in the news due to a video posted to youtube showing him using his sword to protect himself and another man from harm when a fight broke out between multiple people on a bus.
News reporters interviewed him after the video came out. It turns out he has an extensive background in sword training and carries his sword with him everywhere.
Here's the video:
Now, everyone including myself thought it was inevitable that he was going to be taken to jail for carrying that sword with him and threatening others with it. But as I learned, in Arizona it's perfectly legal to openly carry knives of any length and any kind, including swords, so long as you're 21 years old or older:
My advice to you would be to ask your local Texas state congressman to look into this and see if this is something he/she would be willing to take up in congress.
Arizona's laws could serve as a template, making it easier for your congressman to write new Texas legislation.
Also, the fact that this has been legal in Arizona since at least 2012, from what I gather, means that there should be some statistics available regarding crime with knives before and after 2012, or when the law went into effect. You would want to research this ahead of time, before approaching your congressmen. They will want to know how legalized open carry of knives has affected crime statistically.
Statistical analysis is a nuanced and complex subject, of course. Teasing truth out of the data often requires a math and science pedigree at the Ph.D. level. But don't worry. A simple analysis is sufficient to get the ball rolling. Delegate this task to someone else if it's not something you're capable of.
If your congressman doesn't seem interested, that's when you should try other congressmen. And try getting as many signatures as you can on a petition that you write up. Politicians usually pay more attention when a large enough number of people are involved.
You might also want to research the public positions your state's congressmen may have on open-carry legislation of firearms to see how they might feel about extending that to bladed weapons. Those that have come out strongly in favor of it in the past may be more inclined to take up this legislation than others.
Hope that helps.