benefits or risks for leaving one ovary

I am 56 and have been menopausal x 6 years. Due to thickened endometrial lining and severe cramping my gyn gave me option of having hysterectomy which I chose to do. I also have severe pain in right lower quadrant (US looks fine) but he has said he will remove right ovary  to help with pain but also wants to remove the left ovary.  Due to a strong family history of breast cancer and heart disease, I do not want to go on HRT. Would it be reasonable to leave the left ovary - would it still be producing some hormones at this point?  I never had any serious symptoms with natural menopause,  I have tried to research this questions but have been unable to fine much information. Thank you.