I am a female, non-Muslim attorney. In my work, I often meet several other attorneys at a time, and the accepted and expected greeting is to shake hands with each of them as we do introductions. How should I handle it when it seems likely that one of the males I am greeting may be Muslim? It seems quite rude to go around and shake hands with everyone except one person. And even to do that, I would have to assume that I can accurately guess someone's religion from his name, appearance, skin tone, etc., which has all its own problems and just feels wrong. (For example, many people assume from my Italian heritage and last name that I am Catholic, but I am not.) Complicating the exercise is the fact that I practice law in a region with both a large Muslim community and a large Chaldean (i.e., Christian) community. While I have learned to recognize some differences between these communities in terms of common last names, I have no confidence in my ability to "guess" accurately. Also, as your excellent general answer about shaking hands explains, some Muslims do choose to shake hands in such a situation, so I don't want to assume.
In the past, I have always just extended my hand and figured that if the male I am greeting is a Muslim who doesn't shake hands with women, he will decline. No one has ever declined in a business setting, which makes me wonder if I am putting someone in an uncomfortable situation where they feel pressured to do something they don't want to. (I first learned of the custom in a more casual setting where the man just said, "I don't shake." Not understanding the cultural reasons and assuming he had a fear of germs, I stupidly offered him a fist-bump. He explained.)
How to handle this ambiguity appropriately in a business setting where hand shakes are expected? I don't wish to offend anyone either way.