Most people who are inexperienced at cleaning game think that bigger is better when it comes to knives. Nothing could be further from the truth. The best skinning knives have blades that are no more than about 3 1/2". Some of the best skinning blades are only about 2" long. When skinning, you want the blade to be an extension of your finger.
Then, when it comes to actually butchering the meat, switch to a longer bladed knife.