I used to really hate it when I had to cope a bird. I had this in mind this time around while raising my per x prairie tiercel and I paid close attention to what has worked when I have raised puppies. To make it easier to clip their nails I have found that playing with their feet and getting them used to the clippers as young as possible makes life a hell of a lot easier. Keeping that in mind, I regularly touched and held my bird's beak. Sometimes from the outside and sometimes with the beak open and my finger wedged inside. Now he tolerates that easily and doesn't even pay much attention when I do it. I also ditched the idea of files, dremel tools and all the other implements of mass destruction and opted to use the straight blade toenail clippers that McElroy recommends in his latest book. They can be hidden in your hand so the bird doesn't even see them. I can now hold his beak and clip away. I had to to this for the first time the other day and it was remarkably painless for everyone involved.
Moral of the story: Touch and grab your eyas's beak as part of the imprinting process and you will not regret it.