What is the device? A bit more info on it's inputs would help.
You can't connect the Arduino directly to the 9V inputs, even if they're CMOS inputs with no pullups. 5V is probably not high enough to register as HIGH.
You could use pullup resistors to 9V on the device inputs, (if they don't already exist), then a pair of 8-channel open-collector arrays like the ULN2803 IC. It uses Darlington transistors for high current applications, but would work fine for your purpose. There's probably a 16-channel chip that's similar too, but you'd need to search. I can't think of one off the top of my head.
You could use a pair of shift registers with open-collector outputs instead too, to save pins, and clock the values into the shift registers. Something like a TPIC6B595. (Again, really intended for higher currents, but they'd work fine.)
Someone else might be able to suggest more suitable ICs.
Edit: You could use 11 independent NPN transistors, too, but a couple of ICs are probably a better idea.