I went to a lecture about battings and the woman tested all kinds of battings. I know that she said cotton didn't burn like the poly stuff does, it was a much lower flame and slower. But she said that Wool batting was the best for baby ones because it will put itself out. She had a 4x4 square and set it on fire, and watched it. The flames were out and didn't smolder like the other battings did.
If it were me I would use the wool battings. they are harder to find but for the safety of my child. I found some and I'm going with that.