Are there any accounts of people accidentally slidding their throats? I imagine the straight razor combined with limited access to mirrors was a dangerous combination...
He didn't slit his throat, but John Thoreau (Henry David Thoreau's brother) died from Tetanus as a result cutting himself shaving. I'd doubt that many people have slit their throats shaving, but dying from a small nick due to sepsis or tetanus wasn't unheard of.