The $2 PC case fan wins on both price, power consumption and quietness, and seems able to filter a roomful of air in an hour or so.

You must have very clean air already if such a puny fan would be able to keep particulate levels within acceptable limits. In winter, my Xiaomi purifier with a quite powerful turbine fan (or whatever those things are called — they're optimized for pushing air through dense filters) is barely able to keep PM2.5 within 5-10 micrograms on max speed (with doors and windows closed). A PC fan would make approximately zero difference, on or off.

You will spend a bit more buying a few of them, a 12v power adapter, and the shell to tie everything together, but you are correct.

If you buy the cylindrical air filters, you can pop one on a table, pop a case fan on top, and hook it up to a phone charger via a 20 cent Usbc adaptor.

As a bonus, the USB-C PD adaptor has selectable voltage (5, 9, 12v) on little dip switches, and that can be used as a speed control for a 12v fan.

Turn it up to max when cooking, and down to silent again when sleeping.

No need for any fixings or case or anything.