A related question was recently on The Workplace, and one of the answers there offered a phrasing I like. While dodging the physical interaction (more about that in a moment), you can say "I'm sorry, my religion allows me to shake hands only with my wife" (or husband, for women in this position). Or you could say "touch" instead of "shake hands with" if you need the extra bit of brevity, but in this case I think being more specific will actually be less confusing.
As the author of that answer said:
Note how I worded the explanation in such a way that it comes across as, 'this is something reserved for my wife', not 'this is something not for people like you' - the positive side, not the negative side. Pro-wife not anti-women.
Even if you're not married you can use this. If you don't want to do that you could say "future wife", but in a business setting I don't think people are likely to care about that precision. You usually don't jump to discussing family status immediately after meeting a client, after all. If somebody asks after your wife later you can clarify then.
As for the dodge, to avoid the awkwardness (and prompt the woman to withdraw her hand) you need to respond physically in some way. A nod works, or the hat-tip in this answer, or a brief non-contact gesture with your hand -- the important thing is that the physical protocol is pretty deep-seated among those who aren't shomer negiah, but you can divert the exact nature of the physical component.