You definitely have the right to tell or not tell whoever you want about your cross dressing - but, this is your wife's best friend, the person she probably goes to for her good and bad moments. Maybe she wanted to keep her relationship with Kathy free of having to think about trans stuff. Maybe she had held back from telling her because she worried it might change their friendship. Maybe she didn't tell to give you a little privacy with people you know and would have really liked to confide.
Now, your wife will never have another conversation with her best friend without that elephant hanging around in the room. It might hurt her friend that your wife didn't tell her. It certainly will hurt your wife if she finds out from her friend that this conversation happened rather than from you.
If it's okay to tell a certain person, shouldn't it be okay with giving your wife the heads-up beforehand? If you can't let your wife know you are telling her best friend, maybe your reasons for sharing are not good enough.