Hormone therapy and Ovarian Cancer risk

Thank you for your good question. I’ll try to to distill the essence of the findings.
New analysis of existing data (analyzed by individual women in cohorts from around the world) now show that even short-term use of menopausal ovarian hormone therapy (HT, estrogen alone or estrogen with low dose progestin) increases the risk for ovarian cancer by about 50%.
That risk persists for five years—if a woman took HT for 10 years a small risk is still present 10 years after stopping. Given that ovarian cancer has a high mortality rate, one woman extra would die in 1700 women taking HT for five years.
The authors of the editorial basically say that there is no safe use of HT.

That implies that women must suffer with hot flushes/flashing and night sweats (vasomotor symptoms, VMS).
Although we don’t have enough data on women with VMS treated only with progesterone to scientifically prove this, I believe that progesterone alone will not carry that risk for increased ovarian cancer because it decreases the persistent cell growth and inflammation that are associated with ovarian cancer. Besides, many non-hormonal and healthy lifestyle things improve VMS. These include stopping smoking or decreasing weight to near normal from overweight-obese (if these are relevant), increasing exercise, practicing relaxation and believing that the VMS are something with which you can cope that will eventually go away.

I hope this helps answer your question.