If you are left with no choice here is a thought and it is just a thought that came to mind and don't know why exactly. Just trying to think of anything somewhat sensible that could work with this situation. Catch/inactivate those monster nanoparticles.

Empty a bottle of saline nasal spray. Fill it with vasoline and squeeze it up the nostril to provide a slime coating. Wipe away any excess that is at the nostril openings. Breath thru mouth until the moments just before the testing so as to keep a slime coat intact and also so they don't notice anything out of the ordinary going on that would raise some kind of suspicion.

Still giving thought to any of the particles that would end up going down back of throat though. Could be that even if they do that they would just go thru one end and out the other, but can't be certain of that. Still thinking about that part of it as a potential problem.

Practice doing it a few times prior to going for the actual testing. Bring lots of tissues for leakage and for blowing out afterwards and also once blowing a lot out can do follow up rinsing with actual saline spray.

Might even work better if you can add just a little bit of the ivermectin horse paste or cream into the vaso. Desperate times call for desperate [counter]measures.