I was amused by the notion of creating a complicated DIY capacitive-discharge welder just to make thermocouples.
When I worked at the GE Aircraft Gas Turbine Component Test Lab in the early 1950's we had a very simple but effective way to make thermocouples.
We had a little jar containing a pool of mercury covered by a couple of inches of kerosene. The mercury was connected to the secondary of a low-voltage filament transformer 6-12V. The two wires of the thermocouple were twisted together and connected to the secondary of the transformer. The jar had a lid so that the kerosene didn't evaporate when the apparatus wasn't being used.
We twisted the wires together and dipped them in the kerosene. When they touched the surface of the mercury, an arc occurred that welded them together in an oxygen-free environment. The kerosene kept any mercury vapor from escaping, kept the parts not being welded cool (such as insulation on the wires), and evaporated from the finished part.
We made hundreds of thermocouples this way. The junction was a nice little bead and the insulation was unburned and un-frayed by any mechanical manipulation. Best of all, it only took a second or two.