I think it’s fine the way it is. Did Jesus make his disciples clean their hands before they touched him? Is a dirty hand worse than saliva and gnashing of teeth before sliding down the esophagus into a contracting pit of acid?
The sign of peace can be viewed as another way of being the body of Christ before we eat the body of Christ. Like I said, I think it’s fine. I don’t find it a distraction, nor do I find it a time for socialization.