A TDI welding certificate is for topside use only i.e. it is acceptable for welding work on surface.
The CSWIP 3.1(U) and CSWIP 3.2(U) are qualification held by Qualified commercial divers who has shown competency in performing underwater CVI, GVI , usage of Underwater inspection tools which include MPI performed on underwater welds.
You would not get a welder to inspect his own work. You will have a third party qualified personnel to do that. This is where the QC comes into play.
I hope this can help you in your quest.
P/S : If your project is in Australia, you should be looking at their union...cheerios...