There isn't a way to exclude potential visitors from AdWords based on whether they searched using a search operator.
However, most people don't know how to search using operators. The average person won't be using any of them. People who use these mostly include SEO's and search system developers and maybe Library Science majors or professional researchers. You probably aren't losing a lot of money by showing ads to these people once in a blue moon.
To prevent having these ads cost you when you or someone from your company is doing a search using operators, use a CPC rather than a CPM plan. (It'll decrease the chances of users draining your budget with wasted impressions in general.) You can also exclude your own IP address; you won't see ads live at all, but to test your ads you should be using AdWords preview tools anyway.
You can also use audience pools (retargeting audiences; locations) and try to bid on those rather than a more general population.
None of this will absolutely prevent your ads showing to someone who uses search operators, but it'll narrow the chances even further.