Depending on the size of your organization you should have an EEO coordinator in the HR dept. If not you should have someone there assigned to EEO issues. Sometimes it is a group of people with a label like "Employee Relations". Basically you just call HR and ask them if you can set up a confidential conversation about a sensitive matter related to EEO.
In this meeting (usually it will be one on one) you should ask them what would be the ideal way of notifying your coworkers ahead of time who might be alarmed by your arriving at work presenting as your preferred gender so as to cause the minimal disruption to operations. Feel free to tell them how much you love working there and how you wouldn't want to cause any disruption or misunderstandings.
Document that this meeting happened. Document what script they gave you to follow. Follow their script for "coming out" to your coworkers.
Basically, if you do this, there is no way in hell the company could possibly hope to use your identity or any activity related to your identity as an excuse to penalize you. You would have basically asked the company how they want you to behave, behaved accordingly, and then gotten fired for it, and that is wrongful termination irregardless of whether they are bound by anti-discrimination laws.
Also, I recommend storing the documentation somewhere other than the company. Emailing a private email account could be a good way to ensure the documentation gets timestamped.
This may seem paranoid, but yeah, this is your job we're talking about right?
Also of course be aware that the fact that EEO policy is anti-discriminatory toward your class does not guarantee that your coworkers will not discriminate.
Be sure to document any discriminatory activity during and after coming out to your coworkers as well. If one of your supervisors decides to "go nuclear" and fire you, you will need this.
-Anna