Use 10 speed and 11 speed chains for most efficiency with the corresponding 10 and 11 speed cassettes. I am using "10 speed" crank with 11 speed everything else and works flawlessly so you should be fine. I don't think you really need a new crank. I haven't used so called 9 speed cranks with narrower 10 speed chain but I suspect that will work fine for the buyer as well.