If the infected blood of the carrier were dry by the time you came into contact with it would minimize risk. As far as I know Hcv dies if the blood is dry - ask your doc, and its easy enough to run a test - and if you had it, Ab should be present within a couple of weeks
Hepatitis c is transmitted blood to blood. So if a hep c infected person's toothbrush had blood on it and it was used by you and if you had an open sore or bleeding gums then there would be a risk. The same applies to razors - there has to be a blood to blood contact. Without a blood to blood exchange there is not a risk of transmission.
What is the likelihood? I really can't answer that but partners are advised that they should not share razors or toothbrushes because there is a risk.
Mike