I'm not an attorney - see one.
In Penal Code Chapter 46.01 Definitions.
"(1) "Club" mean an instrument that is specially designed, made, or adapted for the purpose of inflicting serious bodily injury or death by striking a person with the instrument, and includes but is not limited to the following:
(A) blackjack; (B) nightstick; (C) mace; (D) tomahawk."
By mace, I believe they mean the old ball and chain - not the pepper spray.
"Penal Code 46.02 Unlawful carrying weapons.
(a) A person commits an offense if he intentionally, knowingly, or recklessly carries on or about his perosn a handgun, illegal knife, or club."
It is my understanding that our TX CHL let's us carry a handgun but NOT other prohibited weapons.
Again, I'm not an attorney - this is a layman's opinion.