Having once read that electronic dust precipitators create ozone, I
asked my sister-in-law the chemist whether bug zappers would do the same,
and whether this would result in a faster oxidation rate for museum
collections.  Her reply follows.

Ozone is produced (among other means) by electric discharge on oxygen.
Air will do.  So yes, every time a bug gets bbq'ed, a little ozone gets
made.A very little, most likely, given the typical specs of bug zappers.
Ozone is one of the strongest oxidizers around in water, or in humid air.
Not so good in dry air, but still far more reactive than plain molecular
oxygen.

The questions will be, how much ozone is produced?   how long will it
persist before reacting with something?  and what is it most likely to
attack?  The answers are not much, not very, and whatever is closest.
You could put lots of something easily oxidized right near the thing to
react with all the ozone and thus protect your good stuff.  You would not
ever get a building-wide concentration of even ppms of ozone, like does
happen at street level in a big city on a smoggy day.

The bigger question is, what sort of bugs is someone trying to eliminate?
Is there a better, more narrowly targeted, way?  Perhaps one involving
evil chemicals?  The only critters reliably drawn to an unbaited zapper
are moths.  In a well-lit museum, even they might not be.  Use mothballs
(naphthalene or para-dichlorobenzene).  Pheromone attractants can broaden
the appeal of a zapper.   But if you go that route you might be better off
skipping the zapper.  Just put the pheromone in the parking lot to draw
the bugs out of the building.  Better still, put it in someone else's
parking lot, since it will attract more than just your building's bug
inhabitants.

Anne