I think the best way to deal with this project would be to case skin the rat and boil the bones.
to case skin make one long slit from the back of one hind leg across just under the anus to the back of the opposite hind leg.
then hook your finger between the leg and the skin and pull the hind leg out of its skin, first one then the other. At this point you have to decide whether you want to keep the feet and claws or not, if not just pull hard and the skin will tear away neatly around the 'heel' leaving the skinned rat with little furry 'gloves'
if you want to keep the feet you need to carefully skin as far down the foot as you can until you reach the base of the toes then snip the toe bones though with a pair of wire cutters, this will leave you with a skin with feet
once you have dealt with the back legs trim the skin neatly away from the anal opening and the tail (which on a rat you wont be able to skin out) and pull the skin towards the head as if pulling off a sock, it should come of fairly easily.
when you reach the front legs keep pulling the skin towards the head untill you can see the where the front legs join from the inside, grasp the and pull them out of the skin.
when the front legs are out you will find that the skin with come of easily till you reach the neck, but no further. now you need to decide whether you want to keep the face, ears, nose etc attached like a bear skin rug. if not then cut off around the neck.
if you want to keep the skin from the head it gets a bit tricky, use a scalpe blade to cut away the skin from the flesh where it attaches around the head, pull the skin taut and carefully cut it from where it adherers to the skull, keep doing this till you reach the cartilage of the ears, cut the cartilage off as close to the skin as possible then proceed with great caution around the eyes cut the nose close to the skull and finally fee the lips.
you should now have an inside out rat skin, scrape away any flesh and fat until you have a clean skin and put somewhere dry and warm where flies etc can get at it.
when dry it will be a bit like furry parchment, it is now 'hair on rawhide' and probably need no further treatment for what you intend to do.
note that as rawhide it will turn back into a soggy skin if you get it wet, you could smoke or wax the inside of the skin to help stop this but it is probably unnecessary.
remove all the meat you can from the bones, could eat the rat meat if you wish, though I would suggest you dont as you dont know why it died and rat does not taste particularly good anyway.
boil the remaining skeleton (which will be minus a tail and toes if you left them on the skin or complete if you didnt) thoroughly until all the skin is removed.
remove from the water and make sure all the remaining tissue has been removed, then dry (and bleach if you wish)
the parts of the skeleton may well be coming apart at this point, keep track of where all the bones go. Separate any bones which look like they might come apart in the future (legs, ribs etc or to be thorough you could seperate them all) paying close attention to how they went together (use a digital camera)
now if you want a really professional look you can coat each bone with clear varnish at this point before reassembling the skeleton using super glue to attach the bones in their original position and keep the rat in the desired pose.
