It is theoretically possible that hair clippers could pass on hep C but it remains very unlikely. Firstly, any blood that was on the clippers would have had to come from someone with hepatitis C virus in their blood. General population prevalence of hep c is around 1.5% in most western countries, so that already cuts down the odds any blood could have been contaminated. Secondly, hairdressers/barbers have very strict policies around infection control these days. So, not sure what the proportion of dodgy barbers is but it probably isn't very likely that your already unlikely to have been contaminated clippers weren't cleaned properly. Thirdly, hepatitis C is a fairly fragile virus that breaks down relatively quickly on surfaces particularly even in spots of dried blood. Finally, the intact virus in liquid form blood has to find its way into your blood stream. A cut on the head (even a tiny one) bleeds quite a bit which is likely to provide quite a lot of resistance against any virus on a clipper blade surface. It turns out that Hep c isn't transmitted very well with solid things but requires transmission by insertion of a hollow instrument like a needle directly pushed into the blood stream.
I think the odds are pretty slim that you would have been infected on this occasion!