benchmade brand lube is a good lube. its mineral oil based but is not food safe from what i remember. you could also use machine oil, grease, etc. you could also run it dry without issues.
whatever you use, make sure you use it sparingly. you are not adding lube to make it slick, your just adding it to protect the metal to metal contact. so apply a dot of lube and spread it around with say a q-tip. a very light layer will be applied only on metal to metal surfaces.
i would avoid nano oil like the plague.
for the blade its probably stainless, i wouldnt worry about adding anything to it. if its a high carbon steel i would use fluid film, mineral oil, frog lube, wax's or anything else food safe.