I searched for "knife" starting at
City Municipal Code Search on the San Antonio Community Portal
and found only 2 references. Locking blades prohibited, no mention of fixed blade knives, no mention of blade length other than the TX-legal maximum 5.5 inch blade. So these appear to be the only San Antonio deviations from TX state law which allows concealed or open carry of single-edged folders or fixed blade knives up to 5.5 inch blades, but prohibits daggers, balisongs, and butterflies.
Although folders with locking blades are prohibited, note that fixed blade knives are legal in San Antonio just as they are in the rest of Texas.
Texaspaul, I would carry a fixed blade rather than a folder that can't lock.
Sec. 21-17. Certain knives prohibited generally; exceptions; penalty for violation.
(a) It shall be unlawful for any person to intentionally or knowingly carry on or about his person a knife with a blade less than five and one-half (5 1/2) inches in length, which knife is equipped with a lock mechanism so that upon opening, it becomes a fixed blade knife.
Sec. 21-155. Possession of knife.
It shall be unlawful for any person under the age of seventeen (17) to possess or carry any knife on a public roadway or public right-of-way; on any other property in which a governmental entity has an interest; or on private property without the permission of the owner or the person in control of the property within the city limits of the City of San Antonio.