If the pyx is fully empty, then there would be no contact with hosts. I’m just a little concerned, though, because I’ve seen our collection of pyx containers at our parish. They are not always empty of particles when placed into the storage drawer. I know that ought not be, but some part of me feels concerned that it is a reality that must seen as possible. Then the paper would contact consecrated particles. That is just my parish, though, and my experience. Thorough instruction would help in this matter.
Perhaps, too, I am the sort of person who keeps separate functions in my head for things. The inside of a pyx is a separate space, for a set purpose, in my mind. That’s just me, though. I doubt all would feel this way. A piece of paper outside of the pyx would not bother me.