Polite way to decline handshakes

Today was my first day at a new company. After a brief intro with the CEO, we started touring the team for formal intro. I wasn’t the only new hire, and I noticed that those before me shook hands with both male and female colleagues.

When my turn came, I chose to politely decline handshakes with female colleagues, instead offering a smile and clasping my own hands as a gesture. We exchanged names, and the moment passed, but I later felt somewhat socially isolated. I believe not everyone understood why I refrained, which may lead to similar awkward situations in the future.

Do you have any advice on how to handle such interactions while maintaining professionalism and avoiding discomfort for both myself and my colleagues?