Hi Mike. I too have sleep apnea, and I use a CPAP now. Literally a lifesaver. I also was hesitant to get a sleep study because of worries about the techs seeing me in my night diapers. I was able to do a home-based study with a device my doctor sent home with me.
However, after talking to others online about sleep apnea, I've run into several that have said the same thing--nothing to worry about, they have seen diapers a lot. They reminded me that sleep apnea can result in bedwetting, especially in adults, and so a significant proportion of those who get sleep studies wet the bed. A significant proportion of those wear diapers to the sleep study, especially since they tell you to do your normal sleep routine like you would at home, including wearing the same clothing you always wear to bed, maybe even the same pillow, book, etc.
I don't know if that allays any of your concerns. I'm not sure it would have for me. But it is always nice to know that in situations like this, its not a big deal to medical professionals. They almost expect it given the situation.
Besides, getting the sleep apnea treated is SO WORTH IT. I sleep so much better now, and have so much more energy. Knowing what I know now, I would immediately go get a sleep study, even an overnight one at the hospital with diapers in full display and the embarrassment that comes with it, because it is so much better now. For many people, bedwetting resolves when the sleep apnea is treated. (Not so for mine, but that's ok).
Good luck for whatever path you choose. I hope you find a way to address the sleep apnea. I feel so much better now that mine is addressed.