Well, we know the answer to this in England & Wales prisons, at least:
In 2019 - the latest year for which the data are available, I think - there were apparently 34 (thirty-four) transwoman prisoners without gender reassignment certificates in the E&W prison system. In addition, the total with GRCs was apparently "in single figures".
So that makes a grand total of a maximum of 44 (forty-four) transwoman prisoners in the E&W prisoner population in 2019.
The total male prisoner population at that point was somewhere around 80,000.
So therefore, the percentage of transwoman prisoners as a percentage of all male (ie cisman and transwoman) prisoners is.... wait for it....
0.06%
(So much for the baloney that males heading to prison would declare themselves in their hordes to be transwomen. I guess the BS "polling" carried out by some people was possibly either self-selecting or a lie....)
https://www.bbc.co.uk/news/uk-42221629
That article also points out the fact that transwoman prisoners are each screened very carefully for prior history and for risk, before they are allowed to be housed in a women's prison. And they're managed very carefully once they're there. But I guess that doesn't fit well with the scaremongering, does it?
Oh, and I don't know whether this story has been reported within the thread. Another correct decision from people who actually understand law, ethics and morality (especially when one considers that the cliche about High Court judges is that they're reactionary dinosaurs who are ultra-conservative and non-progressive.....):
https://www.bbc.co.uk/news/uk-57692993
And that article points to two interesting parts in the judges' ruling: firstly, they note that transwoman prisoners in women's prisons are very carefully monitored and managed; and secondly, they note that between 2016 and 2019, there were 97 sexual assaults of women in women's prisons in E&W - but only 7 (seven) - ie some 7% of the total - were carried out by transwomen without a GRC (and remember, the number of transwomen prisoners
with a GRC is very small - in single figures - compared to those without).
So in fact, ciswomen in women's prisons ought to be
very significantly more afraid of sexual assault by other ciswomen rather than transwomen. Who'd'a thunk it?