They do make cans of compressed air which you should never, EVER buy.  They are ridiculously expensive for the amount of air you get, and are very inconsistent: the pressure drops continuously as you use them so you have to constantly adjust the valve while you work, plus if you don't warm them they will freeze and go to no pressure until they warm up again.

For TOTALLY silent air, you can look into a CO2 tank, but the initial cost is high (not so much the tank, but the correct fittings), you have to have someplace to top up, and they are not without certain risks.

Next to silent are the various oil reciprocating airbrush specific compressors.  Bring money....lots of money.

Not silent but relatively benign are the myriad of airbrush specific oiless piston compressors.  I wouldn't call them noisy but they definitely make sound.  Audible in an adjacent room but not objectionable.  Definitely opt for one WITH a tank.