Here's some more research, since I have a tiny ozone generator in my fridge and I got worried:
Ozone concentrations as low as 70ppb are hazardous when you're exposed to it for several hours [1]. Estimates for Ozone's olfactory threshold aren't trustworthy, since you go nose-blind to it pretty quickly [2], but it seems like it's probably around 20-40ppb before olfactory fatigue sets in [3,4].
My takeaway is that Ozone generators for rooms/basements/etc are definitely a bad idea. The best-cited olfactory thresholds are all in the same order of magnitude as that 8-hour hazard threshold, and with nose-blindness being a significant factor, you just don't want to mess around with that.
Inside a fridge, though? As long as you don't actually smell any ozone when you open the fridge, and you don't just shove your head in the fridge for hours on end, I'd think you're probably fine.