Is it proper for a muslim man to greet a muslim woman that he doesnt know. greet meaning as salaam alikium?

I am under the understanding that it is fine as long as it is not overbrard or in any type of suggestive tone or way that would make the sister uncomfortable. It is the greeting of the people of paradise so I haven't heard of anything stating other wise. Additionally though, women are not expected/obligated to seek out non-muharrams (strange men) to give salaams due to 'shyness' and modesty of speech (sound of voice/interaction)-And Allah knows best