Arduino Mini 05 and battery

I have an Arduino Mini 05 Accessories — Arduino Official Store and need to use battery power. I see that I can use 7-9V on the +9V pin.
However any new battery always give a bit more voltage than its spec. So a 9V battery gives a bit more. Is this within the operational scope or do I need to use another battery with a lower voltage spec?

I'm looking at the schematic and the regulator datasheet - I think it should work. But be aware that you can't get much current from the rice-grain sized regulator they use, though.

The reg is rated up to 16v, the reason for the lower max voltage spec is that as a linear regulator, all that extra power (current * (input voltage - output voltage)) is getting dissipated as heat, and that tiny regulator can't dissipate very much heat.