Caring for wood stock

One of my air wolf stocks seems to be “drying out”. I’m assuming it needs to be oiled? I usually get synthetic stocks so I’m new to this….

I was reading to use conditioning oil or walnut oil or linseed oil. Does that sound about right?

I’d be putting it on 2 walnut air wolfs, a walnut s410, and a walnut cz rifle.

Thanks!