If a male non jew extends his hand to a jewish women, may she accept the handshake?
Although it might be permitted to accept the handshake nevertheless she should try to the best of her ability to avoid getting into such a situation.
Perhaps she should explain that she is not permitted to shake hands because of religious constraints and apologize for any embarrassment or discomfort this may cause – it is nothing personal. My experience has been that usually nobody,feels offended. They may think it’s strange – but when you adhere to halacha, there is no chillul Hashem (desecration of G-d’s honor).