In general, I believe it is generally accepted that if the workers are under your direct control with regards to scheduling work, directing their work, power to terminate them, etc, they would be considered as employees. If you do not schedule their work, do not direct them how to do the work, and can not terminate them, they would be contractors and responsible to qualify their own procedures and welders.
This gets some contractors into trouble with the IRS and state agencies when they classify people under their direct control "contractors" so the contractor doesn't have to pay worker's comp, federal withholding, and social security taxes. I guess you could use similar guidelines as to whether the individuals are employees working under you banner and using your WPSs or subcontractors responsible for their own documentation.
Best regards - Al