It is up to you. There is no hard and fast rule about it. However, to be realistic, as a layperson I would not wear it around my neck. Perhaps because it is quite cumbersome but more so it is an object to be used for praying. Wearing it publicly around your neck can invite questioning look, which you may want to be without. I often have one inside the small pocket of my trousers. It comes in handy when I want to pray the Rosary anywhere anytime.
I’m on the fence with this one as I understand and can see the points on both sides. Personally, I don’t wear my Rosary. To me it is very special and since it’s been Blessed is very Sacred to me thus, I treat it as such. It is placed very carefully in a special box when not in use. But, that’s just me and by no means am I trying to say that people who do wear them don’t consider them Sacred as well. Over the years I’ve seen several people in Church wear them and I didn’t/don’t think ill of them at all for doing so. Since I haven’t found any firm rules against it, if a person has the desire to wear a Rosary around their neck it is fine with me.
There are more masculine bracelet styles as well. Not quite as traditional but there are options that wouldn’t read as feminine.
I wear a Rosary ring. I don’t think anyone notices it and I always have a Rosary with me!