I don't know if this helps, but you have a less than 10% chance of getting Hep C from a fresh dirty needle stick, so, an exposure to a razor would be a lot less than that...So, the odds are heavily in your favor that you won't get it...good luck...
Hot water doesnot remove HCV. These viruses have a life span and according to their specific naturev and surrounding environment, their life span varies. However, roughly it is considered that after 3-4 days at normal temp, they became clear/harmless, but thats not sure. You should go for your check up soon . Its not neceassary that u get HCV virus from him and if u get it , its also not neceassary that its going to hurt your liver coz in 25% cases, human body itself kills these viruses without any medicine. So keep your fingers cross and hope for the best