I think it's possible that Khelif genuinely believes he's a woman and is therefore rightfully competing in the women's category. If he was brought up as female before finding out later that he was "male" he might simply not have accepted it.
Semenya genuinely seems to believe he's a woman, in spite of his testicles.
"For me I believe if you are a woman, you are a woman," Semenya told the BBC.
"I have realized I want to live my life and fight for what I think and I believe in myself. I don't care about the medical terms or what they tell me. Being born without a uterus or internal testicles. Those don't make me less of a woman. I am a woman and have a vagina just like any other woman."
www.outkick.com/sports/olympic-champ-says-being-born-with-internal-testicles-doesnt-make-me-less-of-a-woman
That's delusion - or at least, a refusal to believe the standard definition of male and female. He's clearly managed to rationalise the situation in his mind so that he can continue to believe he's a woman and therefore has been unfairly treated by the sporting authorities.
It may be that Khelif feels the same way. In that case, can he be called a cheat, if he genuinely believes he's female and entitled to be in the female category?
Even if that's the case, the people around him would know the truth, and would be egging him on for their own purposes (I mean the trainers and Algerian boxing authorities, not his family, who might also genuinely believe he's female).
I wonder when he was first told that he wasn't female? Might it only have been after the IBA tests?
As to him suing someone, if he's trying to sue people who have issued threats against him (eg death threats), he'll have a case. And he wouldn't need to prove that he's female.
But if he's trying to sue people who are calling him male, then he'll need to prove he's not, and that might not end well for him. That might be the reason he dropped his appeal to the Court of Arbitration for Sport, because all his medical details would become public.