Please, don't worry. Again, you can not get this virus by ingesting it. It is impossible. To get the virus, the cut in your mouth should be large and actively bleeding, and your friend's BLOOD (not coffee with some blood) should mix with yours.
This virus needs blood to survive-usually fresh blood. Hot coffee is not a friendly place for it.
When something goes through digestive system, it doesn't go through kidney and lever. First, the substance has to be digested-broken down. Hepatitis C virus is just not transmitted in this fashion. It doesn't happen. You should not even be concerned.
But try to stay away from this "friend".
You don't think ingesting the virus could do this? I wonder? What if i had a small cut in my mouth from flossing? It would go through my entire digestive system including liver and kidneys. Do you still think it is not probable?
Is this for real? I mean, with friends like this, who needs enemies?
No, you can not get this particular virus by ingesting it. It is hepatitis A that is transmitted like this-through dirty hands, contaminated food.
Hepatitis C is transmitted only through blood to blood contact. Your "friend's" blood need to come into direct contact with yours to infect you.