Take a look at this...
https://www.powerstream.com/9V-Alkaline-tests.htmYou will see that, for most 9v batteries, the voltage drops well below 9v almost immediately after a load is connected.
Also, most of the cheap 12v fans available run between 80mA and 200mA. Add a little water pump to that and you are now discharging the batteries in the 500mA range which, at .3mAh for the most expensive 9v batteries, will not make it a whole hour.
Is it economical to pay $10 for a set of batteries when they will only last for maybe one hour and achieve negligible cooling effect? You should shift your project toward proving to the world why such devices are a waste of money rather than compounding the economical and environmental problems by creating another scam product.
Edit: you should also note comment #2 at the top of that web page I linked to. It states that these types of batteries are intended for low current draw, not what you are trying to do. That is probably why you assume they will last longer than they really will under the conditions you propose. It's a bad idea all around
and I don't say that to be rude...