I can definitely see where you are coming from with this question. When using this product it is suggested that you cover their face. I don't have birds myself, but I do have kids, and I can imagine that getting a bird to let you cover their face is a lot like getting a child to do what you want them to when it isn't what they want. Another way you can attempt to avoid their eyes and nares is by spraying them from behind. And although it is going to be a pretty wide mist as you are supposed to spray from 6 to 8 inches away from your bird, you could try to aim to low enough where it isn't going near their face (depending on how big your parrot is, as if it is a smaller breed, that isn't going to be as easy). I think it would be great to hear some other customers give their opinions on it, as well as let you know how they got it to work for their bird.
If you aren't wanting to wait for other customer to put in their thoughts, but would like to get advice on being able to use product, please feel free to contact our Customer Service Department at 1-800-381-7179. You can also email them at CustomerService@DrsFosterSmith.com.