OK, I'm happy(!) to answer this. For science!

It's effing
soul-destroying. Especially since the procedure is almost always performed by a woman, or in the presence of a woman.
[Trigger Alert!!! Description of urogenital examination]If the person conducting the exam is a woman, they always address you and interact with you as if you were female. For me, this is probably the most difficult thing: the social aspect of the nature of the test. There's a camaraderie between women (one that I know many transwomen long for and hopefully enjoy when they experience it) that is completely inappropriate and very triggering for most transguys, who just want to get the job done as quickly as possible and get the heck out of there. It's kind-of like using the toilets: women might want to stand around and discuss their shared experience; but guys don't want to look at or talk to anyone and just want to get out quickly.
Having to spread your legs and accept a bodily invasion from a stranger, but especially a woman whose whole attitude is one of "don't worry dear, I know exactly what it feels like because
I'm exactly the same as you are and all of us women have to go through this!!!1!" is very triggering and distressing. They just want to talk about it and empathise with you, thinking that this will put you at ease - but in many cases, this is the worst possible thing you could do with a transguy in this situation.
I like to think of the bits between my legs as being out of sight and out of mind. I'm ok with using them sexually under the right circumstances and with the right person, but they're definitely not for public consumption and I'm not happy with having to show them to anyone I'm not intimate with. I certainly don't want to think about them or talk about them with a woman who thinks we have a shared experience.
So... they insert the speculum and you can feel it dilate a body part that you'd probably prefer not to be aware of, and then they do whatever exam they're going to do. Once they're done they release the speculum and you might be left bleeding for a couple of hours afterwards, particularly with a cervical smear. Of course, they talk to you all the way through it, trying to empathise with what you're going through... but they do it from a
female perspective, with absolutely no sensitivity to how emasculating it is for a man to have to think about his vagina, let alone allow some stranger to probe around in it.
When the test is done, they offer you a sanitary towel so that it can take care of the light bleeding that we'll suffer for an hour or two after the exam. Of course, most transguys will have painful memories associated with the use of sanitary products, but they are given to us without consideration for how we might feel about them.
For me, it's very difficult to have a smear test without feeling that the person doing the examination in some way presumes me to be a woman. I had my first smear at age 19 and I've hated every single one since then.
[End trigger]So my advice to medics offering urogenital exams to transguys is: we don't want to think about it or talk about it; we just want to get the job done as quickly as possible. You're examining a body part, not my 'womanhood'; please treat it as if you were examining my arm or leg. And if you routinely offer sanitary towels afterwards, please don't talk about it. Just leave one near us and let us choose whether we want to use it.
Hope this helps.