[zoombini]

I would imagine that as it comes with an adaptor for 9v batteries that it will also have a regulator inside it.
Design wise it would be the sensible option to design it with an internal regulation section to teh circuitry so that it maintains a stable voltage for the video section, which is likely to be of a much lower voltage.

So connecting it to a 9V regulated supply should be OK.

However...

Tell us the make & model of the camera also about the adapter, does it appear to have any hidden electronics or is it just a battery clip on a wire with a plug to go into the camera?

we can then look atthe website for it (if there is one) and make a better determination if it should be OK.