With a hairless hamster you need to keep them in a tank for their own safety. I would not use any wood product as even aspen can cause irritation. A nice paper product such as Carefresh or yesterdays news with plenty of soft bedding to keep her warm should suffice. Pine should never be used for any animal. Some say kiln dried pine
is safe but recenty studies have proven otherwise.
You do not need to put anything on their skin. They usually do just fine. One thing you do need to do though is up the protein content in her food as all hairless animals use more body protein fuel trying to keep themselves warm. I would suggest a few good quality puppy kibbles in the cage a week for the extra protein. Not too many, just about three or four, or one a day should suffice. I've seen several hairless hamsters not given the extra protein become very sickly.
I do the same thing for my hairless rats
as well, and it's worked wonders and also keeps their skin supple and doesn't dry them out.