Etymologically I would say it fits. "Smith" means a metalworker, note the relation to smite, which one does a lot in blacksmithing, and "black" refers to the black oxide forge scale the results from repeated heating of the iron and steel (vs other metal workers, e.g. silversmith or goldsmith).

So give they are using more or less the same methods of a blacksmith of yore and the etymology works, they would seem to be a blacksmith to me.