Im confused...
You found a magic fish tank air pump that puts out enough cfm and psi to pressurize a 1 gallon weed sprayer in a reasonable amount of time? Air pumps put out a wee bit of air, and god help them if they have to put out a wee bit of air 2ft into a fish tank.
I think you would be better off with a several gallon weed sprayer that you pump yourself every day or 2. I only use 3-5 gallons a week.
As dhuld said, your best bet is to get a lamp timer and a normally closed solenoid valve meant for a reverse osmosis booster pump. You could even get fancy and install the check valve that turns off the pump once it reaches a certain psi.
So my Ideal cheapO system would be :
The biggest weed sprayers you can afford/fit. Fill it 1/3-1/2 with water.
Pump it yourself every day or 2
Rig the sprayer to always be on
Install an inline with sprayer, normally closed 1/4" solenoid valve hooked to a lamp timer
So when the lamp goes off, the valve opens, and it mists. If you get a cheap valve, the valve will fail/leak, and you will have several gallons of water on the floor when you get home.