My husband has gone off to Wakefield Archives for the day so I can't ask him exactly what he meant. Kellys Directories would certainly be at the Local Studies library or at Sheffield Archives, but I think he was looking more at the mark, which Sheffield Assay office keeps records of. All I know is that is where he goes to find out more about firms from hallmarks, although sometimes he has to go to the Cutlers Hall Archive or even to the Hawley Collection Archives to find out more about metal workers
There are quite a few directories on line here http://www.historicaldirectories.org/hd/index.asp
so there may be some that are relevant to you.
There are more Sheffield related directories online here http://sheff-indexers.thewholeshebang.org/DirectoriesIndex.html
and also a Sheffield genealogy forum where someone might be able to help you. http://www.sheffieldforum.co.uk/index.php
also has some very knowledgeable people on it if you wanted to post a query there.