The voltage will be fine - as long as you plug it into the DC barrel jack, and don't try to wire directly to the 5V pins. The barrel jack has a voltage regulator on it that will convert 7-12V down to the required 5V.
But there's a second reading that you need to look at, not just voltage. The 9V adapter will also have a current rating expressed in milliamps (mA) or amps (A, which is 1,000 mA). The Arduino needs around 25 mA to do its thing, and your adapters add to the total current - maybe 20 mA each again. So if your adapter only provides 50 mA, it won't be able to provide enough current and the system won't work.
The USB port provides 5V, but it also provides up to 500 mA, which is more than enough for the job. If your wall adapter is 100 mA or above, that should be enough. And unlike voltage, a larger number for current is better - that's its maximum capacity of supply, rather than something that will burn out the equiment!