I’ve been in business for many years and I attend meetings and shows as well so I completely understand what you’re talking about. There are several things you can do to eliminate embarrassing someone for not shaking their hand.
You can potentially avoid the issue altogether by holding a ‘bag’ in one hand and a ‘phone’ in another. When people see both your hands occupied they seldom try shaking your hands.
What I do very often is smile and tell them that for religious reasons I don’t shake hands with women and then I immediately tell them that “its nice meeting you too”. This reassures them that you aren’t trying to be rude but rather very respectful. Every time I’ve done this these women were always respectful and understanding and never had any problem with it. In fact many times they expressed admiration for following my religious beliefs.
I think many years ago non Jews were not nearly as exposed to these kind of religious beliefs and therefore may have been less understanding. Today though, there are so many religions and beliefs that people have become more understanding and respectful to others religious rules whether or not they understand or agree with them.