My LINK with Sheffield is that I was born there and spent the first 20years of my life there.
One word of caution dont go scrambling tn places other than Sheffield until you have ruled out that they did NOT originate there.
If they came from Sheffield what is now the Cathedral will need their records scouring for family members if not William. Rule that out first. Their occupations would be helpful.
Have you checked out the Apprentice records over to the left?
Have you looked at Bradfield & Ecclesfield. Not far from Sheffield and many Sheffielders went out there for a "quite" wedding etc.