I say a “Shabbat Shalom,” to everyone I pass by on Shabbat, whether they are a 5 year old, a young man, an old folk, etc. It doesn’t make a difference to me, I just think it’s a nice thing to do. If I don’t get a response, oh well, so be it, moving right along, nothing to see here.
I can understand it to be an “uncomfortable,” situation, when a woman offers a hand shake to a man (&/or the other way around). I’ve seen this happen many times, and it’s extremely awkward on both sides. Some people happen to be more sensitive than others.
I’m not going to side with either party. I don’t know who this person is, where they came from, if they even heard me, or if they weren’t Jewish and I just confused the heck out of them hehehe. If you think of it like that, you will find yourself feeling a little less embarrassed or upset about the situation.