Following the advice on this page, I soaked the deer skull from a week ago in hydrogen peroxide for several days. It is much cleaner now and the sulfurous smell it had is mostly gone.
The decomposition of hydrogen peroxide generates oxygen, which is what makes hydrogen peroxide an oxidant (and also useful as a rocket fuel component)
2H2O2 --> 2H2O + O2
According to Frost & Pearson1, the decomposition reaction is very slow in the absence of a catalyst. Various metals and even rough surfaces can apparently act as catalysts and speed up the above reaction. Furthermore, in the presence of certain catalysts the decomposition mechanism generates free radicals, such as HO. and HO2. that are very reactive. I suspect it is the free radicals, more so than the oxygen, that are responsible for the bleaching and disinfecting properties of hydrogen peroxide solutions.
1Frost & Pearson. 1961. Kinetics and Mechanism.