I'll answer your question about what about someone who genuinely does feel better living as a women and is on the verge of suicide until this decision is made and is therefore much happier? How do we make these people and all women feel safe?
If a man has a mental health problem so severe he is suicidal over the thought of his male body then that is a very sad thing and I would hope he could access services to help him. Maybe dressing as a woman helps him, no problem there.
None of that means everyone should be obliged to say he is a woman. It does not mean women and girls have to accept him as a woman. Nor should providers of women's services have to go along with his delusion. We don't do that with any other delusonal thinking.
Centre the women and girls. Let's say you have a women's hospital ward. The suicidal dysphoric male wants to be in the women's ward. It is reasonable and sensible for the women to say No to making an exception for him. They are ill and vulnerable they don't want a man in there. It is sad that he will feel severely depressed that this reminds him he is not actually a woman and has no right to be in a women's space. His feelings don't trump their feelings, he can't come in.
Think of it this way, if an anorexic person is suicidal because of body dysphoria, Slimming World still won't let them join despite the person saying being on a diet plan is essential to their mental health, despite the person saying they are fat too, despite the person getting seriously upset if anyone says they are not fat and don't belong there. Nobody blames Slimming World or its members for being anorexic-phobic.
Man is suicidal because he wants to have a woman's body and wants everyone to believe he is a woman. My heart goes out to him. Nevertheless the help he needs has to come from some other source than vulnerable women in a closed environment being required to pretend he is something he is not.
To be clear, he should definitely be given help for his dysphoria. However, going along with his delusion isn't a reasonable requirement on women and women's services. Saying no, is a perfectly reasonable thing to do and should be uncontroversial.