The amount of ozone you're making is going to be tiny, most likely harmless, but it's so reactive that you just have to push it through a filter made of any of a multitude of substances (even ozone will react with ozone, which is why you can't buy a tank of the stuff and it has to be generated on site). As mentioned earlier, carbon seems like an excellent choice, since it just turns into CO2 and it'll take you millenia to react any visible piece of carbon away.
Also, in the interests of promoting scientific accuracy, when you do the whole blowing air past a corona wire thing, what you're building should not be called an "air ionizer". Why? Because the air leaving the device* is not ionized. If you get it wrong, you've built an ozone generator, if you get it right, you've built an
electrostatic precipitator, or perhaps more consumer-friendly,
air purifier. Makes dust particles briefly ionized so they stick together and neutralize, clump up and fall out of the air (/stuck to a metal surface in the device). Popular at power stations, rather less proven in the home.
Shameless not-entirely-relevant plug:
my blog post on beeswax candles and their claimed "ionizing" properties. Relevant discussion in the comments about electronic air ionizers.
* Note the careful choice of words!