Thank you for asking your query :
I believe you need not worried about contracting HIV.The probability here is significantly less.But there is always a theoretical possibility that you HIV could be transmitted via the blade and cut wound.
So if you really want to be sure, you need to do a Rapid HIV/Antibody test after 4 weeks (Tests can be positive from 2 weeks). But in some cases it may take upto 3 months for the antibody to be positive.
Also checking again with the barber whether he uses fresh blade is not a bad idea. You can never be sure about many things in the world, IMHO you are not at risk.
Hope this help
With Inputs from Dr. Kalanidhi Selvan , ART clinic GSH.