William Cohen, a former “Republican” senator, is being used by the left as part of an attempt to pressure President Trump to not dispute the stolen election. So William should definitely leave the Republicans, but he doesn’t need a new party - he’s already a Democrat in all but name.
He kept his mouth shut under Reagan. Always voted the right way. By the Bush one administration he was making CFR type noises, and then became a member of the Clinton Administration. He was never a conservative, but wasn’t as bad as McCain.