In portuguese: "Navalha de barbear", or "navalha de barbeiro". I think in brazilian portuguese it is said the same way. In the former african colonies that speak portuguese, I don't have a clue how they say straight razor.
"Navalha" means "razor", "de barbear" means "razor that shaves" or "razor for the purpose of shaving". The 2nd option means "barber razor" because this kind of razor is usually linked to the use of professional barber, I don't know why. :shrug: I mean, we're not professional barbers...