Hi there. I'm really sorry that you are going through this situation and I am sure it is making you very anxious. CA 125 is a marker test, as you are aware. However, having an elevated CA 125 does not have to mean cancer but could also be indicative of a biological state that is abnormal. But it is also a marker that should not be ignored, that I agree with your doctor about.
I think that if you are concerned, and I can understand why you are, I'd seek a second opinion as quickly as possible. I'd also call your doctor and ask them to explain what things 'besides' cancers could cause those marker tests to be elevated and how it relates to the things they know about you. Ask about the surgery to remove an ovary and also if there is anything else in terms of options.
Then see another doctor for their opinion and to ask the same questions.
Honestly, that's what I'd do. I understand about the issue of wanting to preserve fertility, but a diseased ovary or an ovary with things such as lots of cysts would prevent pregnancy in and of itself. Not an expert in that but that is my thinking. At 39, you may need to seek the help of a fertility specialist as well regardless. Women are having children later and later it seems but once we turn 40, especially if we have never had a child, our body doesn't cooperate as much. Which I'm sorry about. But modern medical practice makes pregnancy a possibility for more and more women and at later and later years.
Let me know what you decide to do and keep in touch, okay?