Meaning, you can carry a baton (a.k.a. club), handgun, or illegal knife if you're at home or in your car (or other property that you control.)Sec. 46.02. UNLAWFUL CARRYING WEAPONS. (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 if the person is not:
(1) on the person's own premises or premises under the person's control; or
(2) inside of or directly en route to a motor vehicle or watercraft that is owned by the person or under the person's control.
Although I would agree that the exception in Section 46.15 stating that Section 46.02 does not apply if you are carrying a handgun and have a valid CHL is legit. It doesn't say that it only exempts the 46.02 handgun requirement. It says the whole section doesn't apply if you have a CHL and are carrying a handgun.
Any lawyer worth his salt would be able to get the charge thrown out - but you still risk arrest and need to pay for a lawyer. But... Perhaps at that point you could sue for false arrest & imprisonment since the law explicitly exempted you from the violation.