There are plenty of surgeons who will do surgery without letters, and if you don't need a letter they won't know if you are or aren't on T.
BUT there are plenty more who do require letters as well as other strict expectations of what hoops they want you to jump through.
If you want top surgery without T and letters, try calling up plastic surgeons who do gynecomastia surgery on men. You should have a lot of luck there. I had to call several places but found one surgeon who was very happy to give me a low price and show good results, and then during the consultation I came out to him as trans (NOT a requirement and could ruin the experience, but I sensed this was going well so I did it) and he was happy to work with me.
As for bottom surgery, I know of surgeons who will operate on people who are just androgynous or just want 'clitoral release' done as females not even men, so surely they will work on someone who isn't T. I talked to one such surgeon and got pricing and everything even before I came out as trans!
Now realize that the more complex surgeries have LESS people doing them, and as such there is a much lower chance you will find one of the surgeons who isn't a dictator for the Harry Benjamin Standards of Care. Just so you know, those standards are *not* the law, and they are *not* even a requirement among the medical community! They are something people go by because it eliminates uncertainty for those who aren't sure who is a true transgender person and who might be faking, unsure, etc.
Remember, they were invented a very long time ago back before anyone really knew a thing about transgender people. They were written so that doctors seeing a transgender patient for the first time in their life would have something to base treatment decisions on.
The Whitman Walker Health Clinic is one of the biggest LGBTQ clinics in America and specializes in treating DC area trangender people. I went in and talked to them, described my lifelong identification as male, intense dislike for life as a female, had been dressing as male since I was able to dress myself, prefer a name of my choosing, etc. I told them I was prepared to take as much counseling as needed to get my hormone letter, and then the mental health professional there spoke with me, assessed my mental health and gender identity, talked about my desires, and when he discovered I did not want therapy but was happy to contact him or come in if ever I did want or need it, he informed me of the truth about the HB standards and the fact that I could get hormone therapy without paying hand over fist for therapy I did not feel I wanted or needed.
Many doctors are of the same mindset but some have affiliations with individuals or groups who would be very angry or displeased if they did not follow those standards, so not everyone will be so helpful and they may want you to do a lot of things you don't want or feel the need for, such as testosterone. Just keep looking.
If you have your name and gender changed on your drivers license, this should help a lot. Just going in with all legal documents as male will go a long way with certain people who will then see you've filed your papers and went through official processes and are serious about what you want.