There was a Smith's shipyard/workshop at Glasshouse Street, Newcastle upon Tyne according to the English Heritage website.
Whether it was at Tynemouth or Newcastle, the people to help you are at TWAS (Tyne and Wear Achive Service) at Blandford Street, Newcastle upon Tyne. Their contact details are:
Discovery Museum, Blandford Square, Newcastle upon Tyne, Tyne and Wear, NE1 4JA
Email: archives AT twmuseums.org.uk
Tel: (0191) 277 2248
Fax: (0191) 230 2614
Send them an email, they are usually helpful.
Gen in Northumberland UK