SiriusHardware:
I would use the INH lines as well (so four Arduino port pins per 4051) to make them disappear from the scan lines when they were not actually generating a key press.
Of course, that goes without saying, but the two inhibit/ enable lines are common; connected together, so seven lines overall.
You can always use a shift register if the number of lines becomes a concern.
Addenda: No, you don't of course really need the inhibit/ enable lines because you are not using all of the selected options on the multiplexers, the one controlling four row lines will have four open "ports" which can be selected. You can either use the inhibit, or the third select line to effectively disable the selection, total remains six control lines in all. As we are talking about (old) digital logic, it makes no real difference whether the common line between the two multiplexers is entirely floating or not when disabled.
What may be a concern, and the reason that I mentioned digital multiplexers/ demultiplexers may be more appropriate, is the nominal 250 ohm "on" resistance of each 4051 when operated at 5V.