Alternate Space Matt Buttons Wiring Scheme

I was having some issues trying to work out a way to utilize each of my Space Matt buttons that I had made out of an old Texas Instruments Calculator. The problem was that the V.B. (Voice Box) random DTMF tone generator needs a ground pulse to activate a random tone, but with this type of button configuration where all of the buttons are connected to one wire (in this case ground) and the other buttons individual connections to that ground it was difficult coming up with a way to activate both a device and generate a tone through the V.B. So I came up with this idea. Seen here in my diagram I have two buttons wired to show a way in which they can all be wired in the same way to do just that, activate a device and generate a tone. In my diagram the ground connection through any one chosen Space Matt buttons will activate the relay's magnetic coil causing it's internal switch to close, in this case the needed ground connection from the V.B.'s DTMF tone generator to ground. It's a bit daunting having to use all of those relays but I can't think of another way off hand how to do this. Maybe those small "Songle" I think is the name of them relays would do the trick for this?

Example Image of "Songle" relay.