I was experiencing the showracemenu freeze. For me entering a small room usually didn't help. However there seems to be (at least) two other solutions: If you install the Dawnguard DLC you can find an NPC in the Ragged Flagon who will give you the option alter your appearance. This costs 1000 septims and it gives you access to only a subset of the Race Menu. The NPC will refuse to help you if you are a vampire, however. The mod ShowRaceMenu Alternative gave me full access to the Race Menu via a spell. My game did not freeze. I hope this is helpful.
