One inevitablity in the business world will be that you will be in a group, introduced to some new people, and each one will stick out their hand to you in turn. And at least one of them will be a woman. In Jewish Law, physical touch between the sexes is forbidden. There are exceptions and there are loopholes, but living in a society where casual touching is the norm, and equality between the sexes the expectation, it is hard to be a religious Jew in an environment where business relationships are at stake. I will not explore the underpinnings of this Jewish Law, just it's application.
Ideally, I would avoid all physical contact. But in reality, there is often little time to make a decision between being introduced to some business woman and having her hand thrust towards you. There are a number of ways you could react in this situation. You could ignore the hand, and risk whatever reaction this might create. You could limply extend your hand to meet hers in lifeless defeat. You could stop the introductions and explain your religious restrictions and your reasons for restraining from meeting hands. Or you could run away. None of the above are that easy.
For the official record, I heard directly from HaRav Chaim Pinchas Sheinberg, Sh"lita, during a public appearance in Chicago, say that one should not shake hands, and if he can't get out of it, he should fake a sneeze into his hand, and thereby apologetically refrain from meeting her hand without having to engage in any embarassing situation. That was his Psak/Eitzah. I happen to also be of the opinion that actually explaining your concerns to the person, either at the moment or after the fact, actually generates a tremendous amount of respect in most people, and it will, in addition to creating a Kiddush Hashem, sanctification of Gd's name, relieve you from having to face the dilemma with that person in the future.
But in most cases, you don't have enough time to enter a lengthy discussion. Nor do you necessarily have the capability of gauging whether your response will be favorably received or simply scoffed at. The last factor left is simply understanding a person's feelings. If you can't explain your reason for holding back from physical contact, the person may be insulted. I wouldn't want to hurt another person's feelings. So my default position has always been if you can't completely avoid the contact situation or explain it, best to just shake hands and rely on the opinions that allow it. I don't extend my hand first, and I try and avoid shaking (say by standing opposite a table from women I may be introduced to), but when push comes to shove, I don't want to be the one doing the shoving. Just a little physical contact is more than enough.