It could be done, but it sure seems like a lot of work skinning, tanning, & sewing a LOT of munks to make a rug. I'd imagine that the same rules of tanning that apply to any animal apply to munk skin. So just do a search for "tanning hides" to find the procedure. It's not particularly easy - lotta meticulous work involved in my understanding.
But, it would go nicely with a Costanza Russian rat-hair hat.