Note: you can NOT carry a switchblade, because those are classified the same way as hand grenades.
If anybody knows case law that contradicts this, please let me know.
From 46.15 B:
Section 46.02 (beginning):(b) Section 46.02 does not apply to a person who:
...
(6) is carrying a concealed handgun and a valid license issued under Subchapter H, Chapter 411, Government Code, to carry a concealed handgun of the same category as the handgun the person is carrying;
46.01 just provides definitions, including that of illegal knives and clubs:a) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun, illegal knife, or club
(1) "Club" means 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.
...
(6) "Illegal knife" means a:
(A) knife with a blade over five and one-half inches;
(B) hand instrument designed to cut or stab another by being thrown;
(C) dagger, including but not limited to a dirk, stiletto, and poniard;
(D) bowie knife;
(E) sword; or
(F) spear.