Yes you can.
Penal Code 29615 provides exceptions which allow for a minor to carry a firearm. The real question here is whether the intended hiking qualifies as a "sport" and the possession of the firearm is necessary for that sport. With the examples given in the code I would accept the possession while hiking as one of these exceptions. You can verify with your county sheriff if they feel the same way. An easy remedy is to go "hunting" rather than "hiking". If you are hiking on federal lands then the rules may be different.
Being 16 you only need written permission to carry from a parent or guardian, and to be engaged in the activity or directly in transit to or from it.
PENAL CODE*
SECTION 29610-29615*
29610. A minor shall not possess a pistol, revolver, or other firearm capable of being concealed upon the person.
29615. Section 29610 shall not apply if one of the following circumstances exists:
(a) The minor is accompanied by a parent or legal guardian, and the minor is actively engaged in, or is in direct transit to or from, a lawful, recreational sport, including, but not limited to, competitive shooting, or agricultural, ranching, or hunting activity, or a motion picture, television, or video production, or entertainment or theatrical event, the nature of which involves this use of a firearm.
(b) The minor is accompanied by a responsible adult, the minor has the prior written consent of a parent or legal guardian, and the minor is actively engaged in, or is in direct transit to or from, a lawful, recreational sport, including, but not limited to, competitive shooting, or agricultural, ranching, or hunting activity, or a motion picture, television, or video production, or entertainment or theatrical event, the nature of which involves the use of a firearm.
(c) The minor is at least 16 years of age, the minor has the prior written consent of a parent or legal guardian, and the minor is actively engaged in, or is in direct transit to or from, a lawful recreational sport, including, but not limited to, competitive shooting, or agricultural, ranching, or hunting activity, or a motion picture, television, or video production, or entertainment or theatrical event, the nature of which involves the use of a firearm.
(d) The minor has the prior written consent of a parent or legal guardian, the minor is on lands owned or lawfully possessed by the parent or legal guardian, and the minor is actively engaged in, or is in direct transit to or from, a lawful, recreational sport, including, but not limited to, competitive shooting, or agricultural, ranching, or hunting activity, or a motion picture, television, or video production, or entertainment or theatrical event, the nature of which involves the use of a firearm.