I don't agree with the framing of the question. Men's prisons are typically more violent than women's prisons. So from that perspective, statistically the person is in more danger. However if we only look at that, we would transfer everyone to women's prisons.
You are implying but not stating that there is some extraordinary targeting of trans women by prisoners in men's prisons. I don't know if that is true or not but it seems plausible. My argument is that since prisoners are intentionally kept in a defenseless state, that it is the job and moral duty of prison staff to keep prisoners safe from each other, regardless of who the prisoner is. If a specific prisoner is at unusual risk of violence (like a convicted police officer, for example), then I expect that prisons have processes in place for that.
It just makes your original statement look dishonest. You do not object to the order that places people in danger. You and I both know that prisons are terrible for protecting vulnerable populations. “They should, though” is both correct and meaningless to the person being transferred.
I agree that there are dangers in prisons. But I don't think that prevents us from routine transfers of people between prisons.
I do think that prison officials are responsible for the safety of their prisoners and want them held accountable when they fail to do that, or worse, when they intentionally endanger prisoners.
I can't be more clear than that. I reject your framing.