I'm sorry you are going through this.
The CA125 test is not accurate at diagnosing ovarian cancer. Non-cancerous / benign conditions (including benign ovarian cysts) can cause an elevated result.
The large majority of ovarian cysts are benign and resolve on their own. Ovarian cancer is rare - lifetime risk is 1.3%.
Many women end up undergoing surgery unnecessarily. Not only does surgery itself have risks, many women lose an ovary or ovaries when all that needed to be removed was the cyst itself. Ovary removal and hysterectomy (uterus removal) are two of the top overused surgeries in the U.S. and some other countries.
You are right to be concerned about removal of both ovaries (castration). Gynecologists should NOT even offer this to women as numerous studies going back a century have shown that it does more harm than good in many ways. Studies have even shown removal of one ovary is harmful. It shocks me how many gynecologists continue to remove women's organs.
The ovaries have been shown to produce health promoting hormones a woman's whole life if she is intact (has not had her uterus or other "reproductive" parts removed). Their removal, even after menopause, increases risk for heart disease, stroke, osteoporosis, hip fracture, dementia, memory and cognition impairment, mood disorders (depression, anxiety, irritability), lung cancer, colorectal cancer, sleep disorders, more severe hot flushes, sexual dysfunction. There have not been as many studies on removal of one ovary but there have been some that show it increases risk for cognitive impairment and dementia as well as colorectal cancer. Hysterectomy (uterus removal) has some of these same risks since it impairs ovarian function. It has additional risks and harms since the uterus is also vital our whole lives. It has numerous functions - anatomical (organ and skeletal integrity), sexual, and hormonal. My connections with many women who have had part or all their organs removed corroborate these findings.
Bottom line, our "reproductive" organs work together and have lifelong functions. Removal of any one part (or multiple parts) causes dysfunction and ensuing health problems. The HERS Foundation has some good info on their site.
Your cyst is still small so ovarian torsion shouldn't be a concern at this point. It's very concerning that the oncologist will remove your ovary when all that should need to be removed IF you end up needing surgery is the cyst itself (cystectomy). Based on my experience of misinformed consent and outright deceit, I would abandon both doctors since they don't value your vital ovaries / gonads (the equivalent of a man's testicles). There should be NO need to remove the ovary if the frozen section done while you are in the operating room shows that the cyst is benign.
If you do end up having surgery, be aware that the gynecologic consent forms are usually open ended allowing your surgeon to decide what he/she wants to remove after you are under anesthesia regardless of what was verbally discussed. So you will want to make sure the surgical consent form explicitly states what can (and cannot) be removed under what conditions (e.g., remove only the cyst if the frozen section is benign).
Don't feel rushed into making a decision. The harms and regret of having a part of your endocrine system removed or forever impaired are with you for the rest of your life. For me, it's turned my life upside down.
I wish you the best!