If the equipment is not sterilized between customers and the equipment was use on a person with hep c and then next on a customer who does not have hep c. AND there was a hep c infected blood transfer into the blood stream of an uninfected person it is theoretically possible.
This is assuming they don’t sterilize their equipment. If they do, which they should be doing, then there would be no risk.
Just for perspective if a health care worker should experience an accidental needle stick involving a patient withbknown hep c their risk is only about 1.8% so a risk at a barber shop would be less than that.
The US CDC (Center for Disease Control) recommends against the sharing of personal hygiene items like razors and fingernail clippers to avoid transmission within households.
I would assume the risk for hep b would be similar but you could ask in the hep b forum.
Bear in mind no one here is a medical professional we are a community of patients and cannot offer medical advice this is a support group for those infected with hep c and living with the illness or being treated.
For a question about your relative risk you should discuss this with a medical professional like your own doctor as opposed to random web sites and lay persons on the internet.