This is in the section of martial arts in run&gun.

Unless I missed it martial arts specializations are based on unarmed combat. I would put this one in clubs as a martial art specialization rather then a staff specialization.

That's where they put it, as well (sidebar, page 135). Martial arts specializations can be taken for skills other than unarmed.

With the more extensive rules for Martial Arts in Run & Gun, they "revised" where martial art skill specializations go. So yeah, the ones that are a specialization with an armed weapon fall into the appropriate skill (Clubs, Blades, etc).

Kenjutsu is one of the Run N Gun martial arts that specializes in blades. I'm wondering, though--can you mix techniques for armed & unarmed martial arts techniques?

Do you mean "can you use techniques from two different styles?" I don't see why you couldn't. Sort of like nothing stops a person from doing a kick they learned from Karate followed by a head lock from a wrestling style.

What sort of mix are you trying to accomplish?