I think confusion about antique and replica antique firearms stems from cap'n'ball are not treated as modern firearms by federal law for sale and purchase purposes under GCA 68. That does not change state laws on use or carry of weapons.
I don't know California law, but in Tennessee, while a cap'n'ball revolver is not treated as a modern firearm being regarded more as a curio, keepsake or ornament, carrying one as a weapon meets the definition of the act of "going armed" (carrying practically anything as a weapon outside one's home or place of business). The exception is you can get a permit to carry a handgun (open or concealed) in public and carry of a cap'n'ball would have to meet the same rules as any firearm for carry purposes. I can't imagine California being more lenient on the carry of cap'n'ball as a weapon, although in the 1950s Tennessee handgun laws were as strict New York state outside NYC.
New York has that odd law that a cap'n'ball is not legally treated as a firearm until after it has been loaded, to be fired as a firearm. Up to that point, it is treated as a curio or ornament. IIRC once ever loaded, the cap'n'ball is subject to NY firearms laws even after it is unloaded.