I am not a lawyer, so I can only advise you to seek one out for an answer to your question...
But, I can give a few thoughts. If the keychain knife is in the purse, I would consider it "concealed", possibly "deadly", and a "weapon" in the eyes of the law. If CA. has no restrictions on carrying concealed small fixed-blade knives, then you should be good to go. I carry a Shivworks Lil Loco on my keys, but I carry the keys/keychain in my pocket in such a way that some of the keys and the very small knife dangle over the top of my jeans pocket and rest against the outside of the pocket where it is visible to others, i.e. "plain view". I got pulled over about 2 years ago for expired inspection stickers, and the officer had me turn off the vehicle and hand over the keys to him while he had me stopped. He never said a word about the little knife in the kydex sheath, even when he handed back my keys and sent me on my way, so apparently in plain view, it falls to the rights of open-carry for fixed-blades in my state. I'm in PA., so the laws between our states will vary considerably.