The CA Penal Code says:
12020. (a) Any person in this state who does any of the following
is punishable by imprisonment in a county jail not exceeding one year
or in the state prison:
[...]
(4) Carries concealed upon his or her person any dirk or dagger.
[...]
(24) As used in this section, a "dirk" or "dagger" means a knife
or other instrument with or without a handguard that is capable of
ready use as a stabbing weapon that may inflict great bodily injury
or death.
[...]
(d) Knives carried in sheaths which are worn openly suspended from
the waist of the wearer are not concealed within the meaning of this
section.
So there isn't any exemption for "small" fixed blades. You could wear it up front on your belt (most people won't notice it anyway and it's most accessible up front), then move it to a more discrete position when you're on private property - at home, work, the grocery store, etc.
