From the photo provided, it appears you wish to butt weld an area of the tank wall to connect two existing butt welds along the same horizontal joint, and which must include a vertical riveted lap joint between two plates on one side of the weld joint. As others pointed out, there is no such thing as a "cold weld". Fusion welds require heating the materials within the weld zone to above their melting point.
With your situation, since you have already done quite a bit of welding either side of the location in question, I can't see a problem with using the same weld process to complete the joint. Is your concern about any potential distortion/leakage the welding might produce in the existing riveted lap joint?