No, the skin on your hand is too thick for the virus to penetrate.
Most cases of herpetic whitlow is in health care workers like dentists who put their hands in people's mouths and get bitten, etc. It's not that common, and it's very painful. People who have it aren't generally shaking hands.
It's a good idea right now to avoid shaking hands, or to at least be washing them all the time, but it's not because of herpes.