Thank guys. I figured the industrial compressor would work just fine given you have a regulator for lower pressures. My concern was more in that the compressor I have now doesn't have a tank (something I may have to remedy soon)and if it would be enough to adequately power the airbrush. The compressor constantly cycles on and off at low pressures.
Getting a tank will allow the compressor to run for a longer period until the pressure switch shuts it off and then the compressor can rest until you have used enough air (or rather pressure) from the tank. Getting hold of a tank could be another matter though.
I am planning to replace the (rusted through) tank on my compressor with tanks made from two fire extinguishers, the powder type. According to the specifications they were factory filled and tested to a lot higher pressure than my compressor can deliver.
A larger tank means that you can work for longer periods before the compressor starts up again. If the tank is too large your compressor will run until it overheats.
A car tire (or rather complete wheel) could work as tank as well, as long as it is not too big ....