This code will turn off the web toolbar

Private Sub Workbook_SheetFollowHyperlink(ByVal Sh As Object, ByVal Target As Hyperlink)

    Application.CommandBars("web").Visible = False

End Sub
Difficult part is knowing where to put. If you only want to worry about the workbook with the links in then add it to the Thisworkbook object of that project.
If it's for any link then you will need to create an addin with application level events.