Rabbi Yuval Sherlo has recently answered in the affirmative. He says that embarrassing the woman by not taking her hand is a greater sin:
לכן, במקרה שבחורה מושיטה לבחור יד ללחיצת שלום (וכן להפך), איסור לחיצת היד אשר נובע מההחמרה היתירה בקרבה לעריות, נדחה מפני כבוד הבריות והלבנת פנים. מובן שעל לחיצת היד להיות רשמית בלבד, ואין לגלות בה גילויי חיבה יתרים
Rabbi Shlomo Aviner disagrees, and tells an appropriate story about Rabbi Mordechai Eliyahu zt"l:
פעם נערכה לו קבלת פנים אצל מלכת אנגליה, והיא הושיטה לו ידה, אך הוא נאלם דום והצמיד ידיו לצדדיו לעיני כל בית המלוכה והטלויזיה. בערב התקבלה התנצלות מבית המלוכה על כך שהביכו אותו, ובדקו בספר הפרוטוקולים, וכתוב שאין למלכה להושיט יד לרב יהודי
Once there was a reception with the Queen of England, and she offered him her hand. However he stood silent and placed his hands at his sides in front of the Royal House and television. In the evening an apology was received from the Royal House on that they had embarrassed him. They checked the book of protocols, and there it is written that the Queen should not extend her hand to a Jewish Rabbi.
Rabbi Elyakim Levanon of Elon Moreh has also expressed his opinion on the matter. He is against shaking hands, and has called on the National Religious public to "stop searching for hard-pressed leniencies and to cease justifying ourselves".
I remember my Chabad Rabbi in New Jersey who, when offered a lady's hand, would raise his hand up to his forehead and say, "I salute you".
I am in no position to say who is correct according to Jewish Law. Practically speaking, I think that it is best not to take the lady's hand. One time it may be a little bit unpleasant, but after that people know that you are just that kind of guy and they won't put you in that situation again. One who gives his hand once, will have to give it again and again.