||My husband has managed rather successfully in corporate America for the past 18 years without shaking women's hands.
Try the really quaint, old fashioned gesture of bowing when faced with a woman extending her hand. Women in corporate America are very impressed by it, they feel they are dealing with a dashing storybook hero.
Most of our customers ARE women in senior corporate positions and they give us the business BECAUSE my husband is the "type of real gentleman that they don't make anymore". Half of the time they call me in the office and ask for advice on how to attract such a nice, well mannered man. (I tell them to be nice, well mannered ladies).
Make sure you have the ethics and high level of service to live up to the old fashioned image and I doubt any of your female business contacts will put much thought into whether or not you shake hands. Bowing certainly confers a great deal more respect than a handshake (look at Japanese businessmen) which in our society has become a rather meaningless gesture.
Try it! (you can practice in the mirror until it feels natural - I realize that most people did not have parents who taught them as children to bow or curtsy when greeting adults!!! ).