I would not try building. As an engineer, you know how complex it gets. Better to buy and let someone else build it for you.
I've been airbrushing pro for 36 or so yrs. Since I use them hard for 8-12 hrs a day, I go with the oil-cooled 1 HP or so industrials that they sell you for running nail guns, etc. Too loud for you,I guess, tho I have built boxes out of plywood and lined with several layers of old blanket stapled to inside; always have a small fan blowing air through the box to cool it or you'll burn up the pump. It will knock off half or so of the sound. Also, after building them, I sometimes drape many layers of thick clothing on top and this helps more. ALSO, lay a layer of something ( those stiff foam rubber floor tiles are great) on the floor, set the compressor and box there. The floor transmits a LOT of noise, especially to your downstairs neighbor. Even better, put it in another room and run a hose to your workplace. If you must have silent, you can buy them at chicagoairbrushsupply.com or dixieartcom. Not cheap, but they work. Also, I've noticed at Menards (Lowes, etc), they sometimes, not often, have compressors that use small almost silent pumps and they are reasonable.
Right now on amazon there is a California Air Tools CAT-1P1060S for $104. Gets good reviews. I would put a small fan as close as possible to the pump and blow LOTS of cold air on it to extend life.
Honestly the last time I used a silent fridge type (Air Force brand, a first mover in this area), I burned it up in a few weeks of 12 hr days. Swore them off. Good luck.