If your uterine prolapse has not progressed too far yet, you may be a candidate for a procedure to lift your pelvic organs back into their proper positions -- particularly if you aren't yet perimenopausal. Once perimenopause starts, the ligaments holding up the pelvic organs tend to relax and length, allowing things to drop. Since you're still interested in possibly bearing a child one day, I would think you'd want to buy yourself some time to do that rather than going right to a hysterectomy.
You may want to consult a gynecological surgeon who specializes in pelvic floor reconstruction. If, while you are exploring other surgical options, your prolapse becomes more bothersome, you could always use a pessary temporarily until you feel ready to make a decision.
As for your options for symptom relief at menopause, there are many. I've been diagnosed with breast cancer twice and am still on HRT. While it's true that hormones (estrogen in many cases, and progesterone in some) can cause existing cancers to grow, there is no evidence that estrogen-only HRT actually causes breast cancer. The WHI study data which caused such a stir in 2002 have been reexamined, and the conclusion seems to be that the synthetic progestin Provera may be responsible for the increased incidence of breast cancer diagnoses in women in that study who were on the combination HRT Prempro.
So, these days, DRs are kind of split on whether or not women who are worried about breast cancer should use HRT. It's a very individual decision, based on individual risk and quality of life considerations -- surgical menopause symptoms can be pretty rough on some of us without HRT, and low/no estrogen levels tends to increase the risk of some other conditions, like osteoporosis, for example.
If your DR and you decide that HRT is not for you, there are still other medications and even some vitamins and supplements that can help, especially if you are going through menopause naturally, which is a more gradual process than surgical menopause. One thing to keep in mind when deciding what to do about the prolapse is that in some cases, removing the uterus may cause a loss of ovarian function that can be either temporary or permanent. If your primary concern is avoiding HRT, you may want to try to avoid having a hysterectomy if you can, just to avoid that risk of premature menopause.
Good luck with whatever you decide to do.