I'd be inclined to pick up some Break-free CLP for post cleaning.
Field strip the rifle, and place the components in your shower with a peice of mesh over the drain. Run HOT water over the rifle parts for about 30 minutes, washing parts with a gentle, non-abrasive detergent.
Used to do the same with rifles and section weapons after long exercises using blanks which really tended to build up a grim level of carbon inside the weapons. Hand cleaner, of all things, worked exceptionally for cleaning the crappy thermelt mags. Avoid acidics and abrasives like the plague. Anhwho...
Take the individually cleaned parts out of the shower, dry immediately and thoroughly and finish cleaning and protecting with CLP.
Apply grease where necessary and call it a day.
I recently did half a dozen M1A mags packed in cosmoline, and this worked well for me.
Enjoy your new SKS.
Greg