A lot of fur has fallen to wax paper pan covers. The way I make mine is to cut the edges w/pinking shears, so that the borders are uneven, and this allegedly prevents straight lines from printing thru the dirt. I also wad mine up and roll them around between my palms. This sets a crinkle in the pan cover that hopefully makes them quieter when stepped on.
In truth some of this is simply taken as articles of faith, as the young trappers were taught by the older ones.
I have trapped few places where it was necessary to line the trap bed with wax paper. The few times I have used this technique, it worked well, until extreme low temps were reached.
You asked about a better method, or improvement. One of the simplest things you can do is to switch over to wax paper sandwich bags. Crinkle them, put the trap in the bag, and close it. Cut out the necessary slot for the trigger dog, and you'll have a better package than the wax paper alone or used as two sheets, one bottom & one top. You will also have cut down on your handling time a little.
There have been lots of improvements over the years. Some swear by them, and some swear at them.
A few examples are: collecting dry dirt, and mixing it; mixing propylene glycol one part to two, or half & half (depending on how cold it gets where you trap), and spraying this mixture in alternate layers as you bed and blend your trap;
some trappers dry peat moss, coarse sift it and make a trap bedding material; let's see, CoverHulls; good, dry manure from horse stalls, sifted -- the same with dirt from under logs; what a lot of us consider best these days is waxed dirt. If you need to know how to make waxed dirt send me an e/mail, and I'll get back to you.
The next two weeks are going to be very busy for me. I have a funeral in East Tennessee, followed the next week-end by the SE/NTA at Newport, Tennessee, so, please, cut me a little patience, if I am not right back to you with the information.