It is strictly impermissible, according to Islamic Law.
Muslim men cannot shake hands with non-mahram women, and Muslim women cannot shake hands with non-mahram men.
Their religion is irrelevant.
The Messenger of Allah (pbuh) said: ‘Indeed, I do not shake hands with women…’ [Sunan Nasā’i – 4187]
You cited business reasons with no wrong intentions, the context of this hadith is religious reasons, between the best of creation and the best of any Prophet’s followers, purest of people, cleanest of intentions. Still not permissible.
I have worked in a business environment for a number of years, interviewing candidates, meeting journalists, working alongside male and female colleagues, it can be challenging, but as Muslims we must be confident and proud of our morals/principles and do what is right by Allah and His Messenger, for the benefit of our religion, rather than any worldly consideration.
The way to handle this is to explain that we do not shake hands for religious reasons.
I have found people grow in respect of one who is firmly principled. A very good person to do business with.
Hope that helps.