best way to degrease is to buy a fish tank heater with a built in thermometer and get an old cooler. Keep the water warm using the heater/thermometer, and then put the skull in and water level just to the top of the skull. You can use dish soap, and change it out every few days. Do this for 3 to 4 weeks, and you will be in good shape. Peroxide is one way to whiten a skull, another is a product for pools called softswim C. Its VERY concentrated, and you will need to wear gloves and eye protection. DO NOT get this stuff on you. It will burn and turn your skin white and burn you, so be VERY careful with this stuff. I also suggest goggles and a full face shield to protect your eyes.
Do not use any type of metal pan with it as a container either, plastic only. If you soak the skull in this stuff, it will come out AMAZING white, and will look great. When it comes out, you rinse it in water to remove as much of the chemical, and then set in in the sunlight for a few hours to dry where critters like dogs cant get to it and walk off with your priced mount...LOL
Keep in mind that as you degrease the skull (before the whitening processs) the teeth may loosen up, and you will have to glue them in afterwards. I typically do that as the last step, after whitening.
no matter how much you degrease, over time they will yellow some, and you can whiten them back up using the softswim c again