both will work, if you use either, put a thin layer of dirt over it to:
1, make it look natural
2 keep it from blowing away in the wind, buckwheat hulls will blow away faster then peat.
3, its more natural for a K9 or coon to step on dirt then peat or hulls.
I use peat all the time, I dig my bed, put in a handful of peat and make sure there is peat in all the spaces that the trap will touch the ground, then put in the trap, you can pack peat in around the trap. it will take time but can be done, or you could use a pan cover and not worry about it. make sure the trap is solid in the bed. if not usin a screen cover, make sure there is peat all around the trap inside and out. and then cover with a 1/4 or less of dirt and blend in. if the dirt on top of the trap freezes it will still give way to the weight of the critter when he steps on the pan with the peat under it. good luck and post lots of pics.