Your coworker sounds insufferable, and the idea that she is getting some sort of nicotine contact high from an office over is laughable.
I would just say that you have switched to 0 nic juice, and then if she wants to ....., you can explain that air fresheners have the same chemical (though most people assume we are vaping water and nicotine, and I let them think it). Yes, it's a lie, but you're not lying about the amount of nicotine that you are exposing her to (zero), so I think it's justified given the ridiculous nature of what you are dealing with.
I always explain to people that I vape around what I am doing (they have a right to know what I'm blowing into the air), and if anyone ever expressed concern then I wouldn't do it in an enclosed space with them, but speaking to management instead of coming to you and bringing up FDA approval strikes me as hysterical and unreasonable. How does this person know that they aren't FDA-approved? Did someone vaping in the next office actually concern her so much that she did research?