There is no reason to be rude I work in a non orthodox environment and for the past years have never shook a gentleman’s hand. I politely say I am an orthodox woman and don’t shake hand with the opposite sex. Some are aware of it some ask questions. It has never stopped me from doing my work and making a Kiddush Hashem by being an employee who gives them 100%.
Hatzalocha to you.
There are many other people in healthcare who do not shake hands for the sole reason of exposing themselves to germs..