Harav Y.Y. Kanievsky [the Steipler Gaon] quotes the Chazon Ish as maintaining that shaking hands falls into the category of yehareg ve’al ya’avor – better that you should die than to transgress (see Teharas Am Yisrael, pg. 44).
It bothers me to no end that I see supposedly frum Jews shaking hands with people of the opposite gender, and they make all kinds of excuses for this behavior (such as not wanting to embarrass people, or supposedly having a heter for work).
Do you know what “yehareg ve’al ya’avor” means? The Chazon Ish zatzal held that even if they will shoot you and your entire family, you are NOT ALLOWED to shake hands. Period.