What is the ruling on the discussion that took place between the spouses regarding a woman shaking hands with a man, and does what the husband uttered constitute a divorce, or a conditional divorce?

A husband's statement, "If I were to swear an oath of divorce upon you," or "At that time, I would swear an oath of divorce upon you," does not constitute a divorce and is not considered a conditional divorce. Shaking hands with a non-mahram man is impermissible for a woman. A wife must obey her husband in what is good, without obligating him to swear an oath of divorce.