If the testicles are removed a man can literally expect 0% "sexual function" and 100% infertility... 100% guaranteed.
RE UPDATE 1: Sorry, but without testicles there is no way for the body to produce sperm cells thus making a castrated man infertile. And yes, the prostrate does produce the lion's share of the fluid that semen consists of... but again, no balls... no babies.
And yes, you could go on hormone replacement therapy and you MIGHT be able to achieve an erection, but it's most likely going to be lack luster. if you want a Urologist to answer your questions... go see one. I know that sounds crazy and all, but what's more crazy is thinking there are Urologists hanging out here at Y/A.
RE Update 2&3: Go see a Urologist IN PERSON, explain your concerns and see what he has to say. If you don't like what he has to say, find another and get a 2nd opinion. If you have your testes removed and have not saved viable semen at a reputable sperm bank/storage facility... you will not have children.
Lastly, I do empathize with you as I also suffer from a skin condition, albeit a different one. But having your balls chopped off is not the answer man. I mean... you can do what you want, but if it were me I'd continue to search for a urologist AND/OR a dermatologist who one day might be able to help you manage your condition in a more tolerable manner.
RE ADDITION UPDATES/COMMENTS: As I previously mentioned... it's your scrotum, if you want it removed... have it removed. However, I'd try getting a 2nd opinion from a male urologist, not that a female one is less capable or anything, but a male might be more sympathetic and understanding. If anything, it will confirm her diagnosis.
And it seems to me that a scrotoplasty is at least 1/3 of the way to what you want anyway, and if it should work or make your condition more tolerable... then why not start there. If it doesn't work, then you can still have your scrotum removed.
The thing is, your condition is probably so rare that the likelihood of finding someone here who suffers the same way is slim at best, and doctors don't generally hang out at Y/A, they're too busy doing doctoring to be messing around here. Certainly there are support groups or websites that deal with your condition where you could meet and discuss your condition with others. Ask your doctor(s) about them, ask the drug companies who make your meds, you could even ask your pharmacist or do a websearch to find them.
A wise man once said, "If you're falling off a cliff, you might as flap your arms and try to fly... you haven't anything to lose."