You won't have a problem. As a normal non rechargable 9V battery is a little more than 9 volt, but will be around 9V under a bit of load.
Now normal rechargables are about 8.4V under load, and about9V with no load
Most devices should have an operating voltage range. Might be an idea to check what that is. Im guessing it is between 7.5 and 12