You won't get Creature Products every time you skin a body. If you see a green spark, the product of the specific Monster will appear in the same container as your Obsidian Knife. If you see a yellow spark, you won't get the product. The chance of getting a dead body skinned successfully may vary from creature to creature.
Corpses can´t be skinned starting 10 seconds after death and before the body gets in the second state of decay, after 5 minutes. After skinning a body, it will "rot" one level (to the second state of decay) and won't be able to be skinned again.