How do I get the Cosmoline out of my Mosins wood stock?

[LifeInPa]

I got my Mosin yesterday. It was $150 out the door with most of the accessories, a 20 round box of Silver Bear and the associated fees related with the transfer. Anyway I am thrilled with the rifle: Built in 1938, round receiver, metal and furniture in excellent shape. However the rifle has been soaked in Cosmoline to the point that it melts off onto my hand when I handle it. I have been reading online on removing Cosmo from the rifle. For the metal parts it's widely accepted that Simply Green and hot water will take care of the Cosmo followed by a coating of CLP Break Free will protect the parts from rust. However getting the Cosmoline out of the wood stock gets into a heated debate it seems. I have read so many different opinions and counter opinions on the internet my eyes are about to bleed.

Some say use heat. Not a problem but I won't put the stock in my oven, I don't mind using a hair drier or heat gun but it seems extremely time consuming and the other methods of using heat are too involved or the things required aren't available to me (Hard to use my attic when it's in the 20's). I really want to avoid using harsh chemicals on the stock because I want to maintain the original Russian shellac/finish. I am considering letting some Simple Green sit on the stock and then wiping it down with some hot water/rags (Not going to submerge the stock in water for obvious reasons) but I have concerns about the effectiveness of this method. Will that little bit of water swell the stock and is the Simple Green powerful enough to pull the Cosmoline out of the stock?

Just to let you guys know what I have available as far as cleaning products are concerned:

-Engine Degreaser
-Simple Green (Diluted I believe)
-Break Free CLP
-Hoppes oil and cleaner

Thoughts? Also do you guys have a disassembly guide for beginners? Sadly, I don't have that tool used for breaking down a Mosin so hopefully regular screwdrivers won't strip the screws. I want to get this project underway today. Thanks. Here are two photo's to give you an idea how soaked the stock is in Cosmo: