Someone who owns their own business isn't, by definition, working class, regardless of how they speak, their education, what car they drive, or any of the other witless drivel used by people who don't understand basic economic categories.
The working class is that class who neither own nor control any means of economic production, and exist by selling their labour. An old-fashioned idea, but it has the benefit of a precise meaning, unlike the sociological garbage which relies on analysing people's choice of baseball caps in order to say nothing meaningful about anything.
-- Ian