Letting the air pass through a strong alcoholic solution, as vodka or absynthe.
Alcohol is known to be hostile to a lot of organisms: keep in mind that surgeon sanitize their hands with products based on alcohol.
If you do set up a good turbolent flow without losing too much contact time, you should manage to reduce in great part the microbial count in your airstream.
Geometry of the apparatus, on a budget
The idea is getting plenty of curves, so air has to go through multiple alcoholic phases and optimally a final washing water phase. Getting one more washing water phase in the middle would be ideal.
Stainless steel piping fittings or traps (also called siphons) would be the ideal choice: coupling multiple U fittings will give you this solution for less than 25$, and it will hold to sanitation standards higher than the food industry has.
In technical terms, it'd be called "absorption airstream contamination": ditching sanitizers in favour of strong alcoholic solutions will already make the air more-than-FDA safe, but if you really have an issue with air containing a small part of alcohol, you can place another fitting or trap where clean water will rest.
This process is used in the pharmaceutical industry, for a safety regulation framework of reference.
Using distilled water in this curve would be ideal: it tends to have a very low starting microbial count, and the alcohol it will absorb (thus removing it from the air stream).
If you do choose this solution, I can estimate the amount of water and\or the maximum air flow to get a fixed concentration of alcohol, or if you choose the bubbling solution I can relate the number of curves.
Even when they tell you otherwise, traces of chemicals always linger by the very nature of chemical reactions: the smaller the concentration, the slower the reaction. After a while, it slows so much it practically stops.
Live easy, very small traces can be safely neglected both by taste and health, and I don't mean figuratively: under a certain concentration, there is no evidence that a substance can alter the equilibrium of your body. How low that certain concentration is, however, varies by substance, hence my offer.
Only a few alcohol resistant strands would pass, and they'd have to be more easily dispersed in air than water or liquid phases: competitive growth should hold them back, however.