You may not get any symptoms or maybe they may be mild. Your ovary may have been giving you a small amount of hormones that your body has adapted to.
You might want to just wait and see how you do and then discuss this with dr if symptoms arise.
I understand your concern with cancer in family and about taking hrt.
I am not on hrt and have a few hot flashes. I was in perimenopause(more hot flashes and insomnia then) at 54 when I had my complete hyst in 2003. I took hrt for 1 year and now have been off 7 mos. due to my age and cancer in family.
I am taking calcium, multivitamin, vit. c, evening primrose oil, and vit. E and exercise 3 times a week. My hot flashes are few and don't last long. I have found that deep breathing when one comes has helped so much. I keep ice water near and have a fan on at night when it is hot. I dress with less and layer. I think cotton, no wool or acrylic helps so much to keep comfortable.
I wish you well on your up coming surgery, and hope you don't have any symptoms to fret over.