Thanks for posting this, it's not an uncommon question. Firstly, the reason to give you a hysto is that you're trans and are requesting it. These surgeries are medically required, as statements like the
AMA resolution 122 support.
How to code it for insurance is where it gets more complex... Most insurance policies will deny the coverage if the surgery is related to gender reassignment but if your identification documents have not been changed to M, then you could get it covered by insurance IF there are symptoms of polycystic ovary syndrome, recurring pain, etc. If there are no symptoms and coverage is denied, you can
appeal, and it's possible to have a denial overturned. That's where my knowledge ends though, as I'm not a U.S. citizen.
As to alternatives, yes, there are many surgeons who could perform the surgery, both inside the U.S. and abroad, if you pay out of pocket. In the States, a hysterectomy runs anywhere from $9000 to $20,000 depending on the procedure. In places like Thailand and Serbia, you'd pay much less.
So, you basically have two choices at this point: try to get insurance to cover the surgery, or save up and pay privately to have it done.
I hope this helps!