All you need to attach the AWG#16 Evanohm "plug" to the AWG#20 copper wire is a DIY version of one of these:
http://www.percussionwelder.com/I contacted the engineer that designed the machine. He said that it is DC, not AC or RF. So, reverse engineering what they are doing on their website should not be too difficult; here is a video introduction to the technology (and there also is a video playlist on this machine):
There is a mechanical device that positions the 2 wires together, with a lever that first moves them apart, then back together but with a small solenoid that "slams" the wires together at just the right moment. The videos do not explain the process exactly right; I think they are hiding the details on purpose (they want to sell you a welder, not tell you how to build one). If you are going to weld Evanohm to copper, a plasma-arc is absolutely essential-- nothing else gets hot enough to properly join the materials. If this were a continuous process, then it would be called "TIG" [Tungsten Inert Gas] welding, but it is a pulse of a measured amount of energy; not a continuous arc, and there is no tungsten electrode (the 2 wires are the work pieces and also act as the electrodes); also there is a mechanical percussion that TIG does not have. That said, much of the information on TIG welding dissimilar materials applies here also.
Imagine that you have a power supply that puts put a high voltage at very low current (a large resistor in series). When the 2 wires are touching, this current flows between the wires. When you pull the two wires apart a short distance, an electric arc forms; but because the current is very low (say, 10mA to 100mA) it really doesn't heat either of the wires very much; it is more of a "pilot arc" to keep the gas in between the wires (either air or an inert gas like Argon) at a low impedance. Now, lets say the wires are about 2mm apart at this time, with this pilot arc happening. If we have a large capacitor charged to a high voltage, and then suddenly (through a solid-state switch like an SCR) connect that capacitor to the two wires, there will be a powerful arc formed, and because of the very high current, the arc temperature can exceed 8000K. Probably, the negative arc voltage should be connected to the Evanohm wire, with the positive lead connected to the copper wire. This plasma-arc melts the ends of both wires, and at the right moment, the wires are moved back together mechanically, and simultaneously slammed together with the solenoid. This entire process happens in 0.5ms to 2ms (depending on the requirements). The switch between the capacitor and the arc is a high voltage high current SCR (which also prevents back-feeding the pilot current into the capacitor until the switch is turned on). The energy in the capacitor is
0.5*C*V^2, so you control the energy both by controlling what voltage you charge the capacitor to, and the value of the capacitor(s) for the discharge. The voltage for the pilot arc is simply a high (isolated) voltage (say 100V) going through a high-wattage resistor. The SCR should be rated to 400V at very high amperage. The capacitors should be multiple polypropylene film type, on the order of 100uF (but I haven't tried this or done the math; that may be too much or too little capacitance). You can make a switched arrangement that will parallel 1-10 capacitors to get more range out of the setup. If you are always welding #20 copper wire to #16 Evanohm wire, then the capacitor value and charge voltage can be fixed. The capacitor charge current needs to be shut off before firing the SCR so that the SCR will eventually turn off. Once the SCR turns off, the charger can then be reconnected to the capacitor (using some kind of relay). There needs to be some kind of SCR driver that can provide a fast pulse to the gate of the SCR, and a solenoid driver too. All of this could be controlled by an Arduino or something similar. Oh; and because copper wire oxidizes rapidly at high temperatures, there needs to be an Argon tank, regulator, and solenoid valve that controls the shielding gas at the weld point. The gas is only on just before the weld, and then is shut off just after the weld, so one canister of gas can be used to make many thousands of lead sets. The video does not show using a shielding gas; if you don't use the Argon shielding gas, then the copper will oxidize, and it will still have a mechanically good weld, but it will have a lot of copper oxide in the weld which will create a high thermal EMF connection (which would be very bad).
The price for one of these welders is > US$10000 (and that's just for the butt-welder), so it must be a DIY project.