use “Ms or Mrs”

1. It was Miss for unmarried women before Ms was coined and popularised for “none of your business whether I’m married or not” so Ms was acceptable regardless
2. Doesn’t Mrs look like it’s missing a possessive apostrophe, a Mr’s woman?

And your main point, degender the male pronouns, it wouldn’t work. “Man” used to mean people, male men and female men and child men – boys and girls – had different words, some of which are still around. That’s why people say there’s nothing gendered in “chairman” (which 50 years ago was logically equal to “chairperson”, unless you count other species as people).