My experience is a bit different, but it may help answer some of your questions. I had a total hysterectomy at 45. I'm now 75. The doc thought I might have a cancerous ovarian tumor. It was not cancer, but I was a mess with endometriosis. For the first four years after the surgery I was on hormone replacement therapy until I read an article about the risk of heart attack when on hormone replacement therapy, and I told my PCP at the time I wanted to go off it. It was the best thing I ever did. I had no side effects at all. My hair, skin, my everything was fine and has been to this day. And I did not gain weight.
The recovery after surgery from the total hysterectomy was long and painful, about six weeks. I don't think you will have that experience. I would not presume to advise you, but I think if there was cancer in my family, I would seriously consider it. You are 72, you don't want to be having anything like this after age 75, unless you really need it. The older we get the less ability we have to recover.
I did a quick look on Google and it seems Medicare doesn't cover this if it's preventative, so it's going to be costly. If it was me I'd ask the doc if there is some way she can justify the surgery to Medicare.
Best of luck with the surgery if you decide to go that way. Trust your intuitive sense. I find it's usually right.