An observation from an old timer if I may?
I'm nearly 30 years post-op, but for various reasons which I won't go into (as it is a rather long story) my voice never actually broke and I have a natural contralto singing and speaking voice. Over the decades this has probably saved me from any suspicion many times.
However - my observation is that, within reason, gender perception is seldom actually as much about pitch itself as people seem to think. The attack (whether the sound is harsh or smooth), the intonation, the timbre, the variation in sound volume and quality, the animation of the voice, even the use of language seem to me to be of rather more importance.