Getting your ovaries out shouldn't be that huge of a deal in terms of scarring. I'm pretty sure they can do it with tiny little incisions, or if you get a full hysterectomy they can do most of it through the vagina.
As for other scars, I love Bio Oil. It works better than vitamin E in my experience, though I think it has vitamin E in it. I don't have any surgery-sized scars, but I do have some pretty decent self-injury marks. They're faded to skintone now and mostly flattened out. If I'd actually used it more than a couple times a week I'm sure it would have been even better. Anyway. It's $10 on Amazon and smells lovely. At the worst, it'll be no worse than massaging your scars with any other oil, and it's the massaging that's really good for them.
My partner doesn't mind my scars in the slightest. Where they came from saddens him a little, but as far as marks on my skin, most any decent partner shouldn't care too much. They're mostly all on my forearm, in the summer the ones on my leg show too, and honestly, no one notices. Are you afraid that someone will judge you for having scars? Most everyone has scars.