I just started looking at this for my CNC machine as I have similar needs.
For the money, I am tempted to try one or two of these:
12V, 16CFM, 33mm Blower Fan - RobotShop
They are so cheap that it doesn't matter if it doesn't work.... if they don't move chips I'll use them for extra cooling.
The only way I know of to get near silent high pressure jets of air is to get it from a 3000psi scuba or 4500 psi scba tank. With a regulator, you can get an hour or maybe two per fill. Used scba tanks are cheap. I got mine for $115 with fresh hydro and 7 years of life left.
Obvioulsly this is no good for long jobs and filling them would be a PITA. You can get cheap Chinese 4500 psi compressors to fill them for $500 but it's not very practical overall.
I have an air brush compressor. I wouldn't use mine for this. They aren't great for continuous use and they are not particularly powerful.
I have a cheap electric oil vacuum pump 1/8hp which I got for $50 off ebay (for something else). These are quiet (ish) but fill my garage with smoke / vapor after 30 mins of use.
I have a Thomas oil free 1/2hp vacuum pump and compressor in one. I would recommend this above all the other options suggested here so far. They are rated for continuous use. They are powerful and require little maintenance. My 1/2hp model is not super quiet but it is 20 times quieter and less annoying than my shop vac. The vacuum on it is superior (by miles) and the compressor side is adequate to move chips without needing a seperate regulator.
Used Thomas pumps are cheap on eBay and readily available. I bet a 1/4hp or 1/8hp model would be even quieter and still powerful enough for this purpose.
My plan is to run the Thomas pump from another room so I don't have to hear it. If that doesn't work out, I'll make a soundproof enclosure (aka a box lined with sound-proofing foam).
Btw, don't even consider an electric paint sprayer. I have one that I haven't touched since I got it because it is so loud I can't stand it. It's the worst option here.
Please let us know if you find a better option. I hate loud noise when I work so much that I have plans to build an insulated brick wall enclosure around my CNC machine.