Sure it was them? I couldn't find that on their site, but I did find a 2015 survey report by the National Centre for Transgender Equality which features similar statistics. pp 100-103, table 7.5, figs 7.14, 7.15.

Yes, you're right that the Williams Institute based its statement in 2015 on "data" that comes from that 2015 survey by the NCTE.

But my comments about the plethora of the kinds of surgeries now being done under the guise of "gender confirmation" were not based solely or even largely on the NCTE survey or what the Williams Institute has said. I was just pointing out that even the Williams Institute, which was founded to put out pro-trans propaganda, admitted in 2015 that at least 88% of TIMs (as surveyed by the NCTE in 2015) in the US have not had any genital surgery.

Re your point that

For the male respondents those procedures are all less common and less desired (facial feminisation only very slightly less desired) than genital surgery. The most common are non-surgical voice therapy and hair removal, the latter four times as common. This still means ~60% of the TIM respondents have beard stubble, mind.

As you seem to be aware, online surveys of this sort are not a good, reliable way of getting data, so I don't get why you're placing so much stock into what anonymous respondents to the NCTE survey said. I especially don't trust online anon surveys done on a population of people who base their entire self-concepts on telling lies to themselves and the world, and who are hell-bent on making everyone else lie too.

Also, you are mixing up non-surgical procedures - hair removal and voice therapy - with surgeries. I was very careful in my comment to speak of surgeries only. Not all cosmetic procedures, body-modifying interventions or "gender affirming medical treatments" are surgeries.

But the NCTE survey is sorta beside the point coz there's a lot more information on this topic out there. For example:

A paper called "Demographic and temporal trends in transgender identities and gender confirming surgery" published in Translational Urology and Andrology in 2019 said:

Across transgender populations, chest (“top”) surgery is more common than genitourinary reconstructive (“bottom”) surgery. Chest surgery is generally reported at about twice the rate of genital GCS. In studies that assessed transgender men and women as an aggregate, chest surgery has been reported at rates between 8–25%, and genital surgery at 4–13%.

This could be due to a number of factors. Chest surgery may be more important to outward gender expression for many individuals, as the presence or absence of breast tissue is more readily visible in daily life than are the genitalia. Chest surgery is likely more accessible as well, as most plastic surgeons are familiar with breast augmentation and mastectomy for non-gender affirming implications, while relatively few are trained in techniques required for transgender genital reconstruction.

Genital GCS is generally less common than chest surgery, with prevalence rates of about 25–50% for transgender men (females) and 5–10% for transgender women (males).

So 90-95% of males who ID as trans have NOT had genital surgeries. Moreover, males caught up in transmania are having life-altering surgeries for "gender confirmation" at far, far lower rates than females are. Though clearly this sick movement is very damaging to vulnerable males like Jazz Jennings, most of the sacrificial lambs going under the knife in recent years and today are girls and women.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6626314/

Also, it's very important to note that the situation regarding "gender confirmation surgeries" has changed enormously since 2015 when the NCTE survey you rely on was done. Since 2014, Medicare, various state Medicaid programs and Obamacare policies have started covering "gender confirmation surgeries" and that - plus the influence of the internet and the spread of transmania - have resulted in a huge demand, as well as in many medical practices and institutions rushing to set up transgender surgery programs to meet the new demand:

https://www.nbcnewyork.com/news/local/top-nyc-hospital-racing-to-specialize-in-transgender-healthcare/1227617/

https://www.transhealthcare.org/transgender-surgery-centers/

My statements about the various kinds of surgeries now being commonly done for "gender confirmation" was largely informed by regular looks at what is being published about these topics on PubMed, as well as on information provided by cosmetic and plastic surgeons.

According to organizations like The American Society of Plastic Surgeons, the American Academy of Facial Plastic and Reconstructive Surgery, the American Academy of Cosmetic Surgery - and their counterparts in other countries and internationally - and the Journal of the American Medical Association, there's been a big uptick in the demands for "gender confirming surgeries" since 2000, and especially since 2014, when changes in US Medicare and private insurance rules means more people got coverage through private plans as well as through Medicare and some state Medicaid programs.

Because I have have history of (non-cancerous) tumors on my face and in my eye orbit/socket, I happen to know personally several big-name US facial plastic surgeons and head & neck surgeons who are influential in their fields and aware of trends - and they report that requests for facial and neck cosmetic surgeries and procedures from males for the purpose of "feminization" and "gender confirmation" have "skyrocketed" in the past 5-10 years and are now "off the charts." Waiting rooms that used to be filled almost exclusively with female patients wanting facelifts, nosejobs, eye lifts, cheekbone implants, fillers and Botox are increasingly seeing a surge of male patients wanting to get what Blaire White, Gigi Gorgeous, Caitlyn Jenner and Munroe Bergdorf have had done to their faces.

Here's a video about Bergdorf getting his FFS "to match his femininity." Note it's not done in a hospital: https://youtu.be/y9--ERLfyTY

James Bradley MD, a leading US practitioner of facial feminization surgeries, says that when he started doing the procedures in 2000, there was virtually no demand, but now he personally does one to three such surgeries each and every week and is training US military surgeons to do them.

In the 20 years since he began performing the surgery, awareness of its existence has increased exponentially, significantly thanks to the rise of the internet.

“[Patients] see some of their friends and people on social media having success with it, and they want to have it done,” he said. “They’ve told me that after the procedure, they feel more comfortable in public, and fear less for their safety.”

The situation with insurance has also changed, and some policies are starting to cover the surgery. “There’s still a fair number of patients who need to self-pay,” Bradley admits, but more and more, insurance is beginning to cover the involved expenses.

https://nypost.com/2020/10/21/military-looking-to-offer-feminization-surgery-to-trans-troops/