As for someone who is mute and can't talk through verification, there are plenty of ways to verify without voice. Streaming for a few games with a webcam works. If someone can't do any verification, too bad, they can't play.
It's like having a tournament for United States and someone saying they're a US citizen but they can't show their ID or prove in any way they are American. If the situation was related to nationality, there'd be no question, you'd not let that person play. But since it's gender, and it is so awkward to force someone to "prove" their gender, you don't want to.
I think as a tournament you need to make a decision on this. Either say anyone that claims they are female can play and trust that, or verify everyone and don't be ashamed about it. Otherwise you get this situation afterwards and it's awful for everyone involved.
I'd like to say that I am sympathetic to not wanting to show your face or voice if you're a female but if you want to participate in a high-exposure tournament, that is something you'll have to choose. It is a matter of scale, if you participate in a live LAN it's entirely unreasonable to say to them "I won't play unless you don't show me on camera" because its critical to their event. And being female AND verified is critical to this event, so in my opinion you just need to verify everyone for sure. If they can't, that's too bad, and you'll just have to live with that person not playing in the tour.