What size rafters and what are their spans. A 1x6 spaced sheathing with shakes is a relatively light weight roof. By leaving them, you are adding quite a bit of weight with the sheathing regardless of ply or osb. The presidentials are a fairly weighty shingle as well so you want to make sure your existing rafters are going to hack it.

If the rafters are spec'd for the weight and you leave the 1x's, you could get by with 1/2". Without the 1x's, I would go 5/8" ply or osb. Personally I prefer plywood, exterior grade no less than 7 plies per sheet but in your drier climate, osb is fine and costs a tad less than a decent plywood. In humid, wet areas where you can have condensation concerns, I would steer away from osb.

Thanks for the reply. 2x6 rafters, 24" centers, horizontal span is 10'0.5". AWC website span calculator says that should be okay. I'm using the Presidential, not the Presidential TL, so pretty heavy but not extreme.

The rafter size and spacing is typical for type V construction.
Either 1/2" OSB or standard CDX are sufficient for you application.
Covering the existing 1x will preclude you from having to use CCX at the eaves and overhangs.
California requires a permit for reproofs.

Make a conserted effort to get decking that does not use formaldahyde based glue. You will be a long time getting that smell out of your home plus the fumes can bd sickening.

The waterproof adhesives used in structural roof sheathing panels do not contain urea-formaldehyde and should not affect the air quality of the house.