I've not had this operation, but have had cause to read up on oopharectomy. I'm not surprised you are feeling so anxious.
Ultimately, it's your body and your life, and your needs after surgery are just as important as any other consideration. In my experience the NHS can sometimes be a bit shit at recognising this and responding appropriately. Staff forget that their patients are human beings who exist beyond the few minutes they spend with us. So it's not you that's the problem here and you are not being unreasonable.
Ultimately, your doctors can explain the risks and benefits to you, but the decision should be yours. It is your body and you have to be able to live with the consequences of what they do to it. They owe you a duty of care after surgery, not just during surgery.
I am really not surprised this is causing you anxiety. You have every right to advocate for yourself and state what you want and need in this scenario. Has your oncologist discussed with you their reasoning, what the risks are, what the benefits are, etc? Have you had the opportunity to weigh it up yourself and make an informed choice? Or have they just told you no?
If the latter, then you may need to be pushy so that you are involved in the decision and have all your options explained. The GMC requires doctors to explain the risk and benefits of all the options before a patient, not just to impose their own view on you. So by reminding them of their responsibilities you are not doing anything wrong.
Once you have that info you might feel differently, but at least you might not feel so powerless if you have more knowledge, have taken charge of things a bit more, and have had the opportunity to discuss in depth and find out about all your options. Feeling powerless can make anxiety so much worse.
It's not acceptable for them to put you through such significant surgery with no consideration or planning for the impact it will have on your life. You are a person whose life is valuable, and this stuff matters. Remind yourself of that if you need to push a bit to make yourself heard.