From the schematic it looks like you don't need a potentiometer at all, just a variable voltage.
The "CVS MAX TRIM" and "CVI MIN TRIM" circuits just set the voltages at the ends of R1 to restrict its range. At most the range can be -6.2V to 0V but the trim controls can narrow it down to about -4V to -2V.
The problem you will face is the polarity. On its own the polarity is not important, you can just produce a positive voltage and swap the output wires but there will almost certainly be a ground in the PLC and probably in the welder and linking them together will cause problems. They are probably linked already through the power cords.
There are many solutions to the problem, the simplest is probably to use an inverting op-amp circuit as the load current seems to be quite small. Your PLC would produce say 0V to +6.2V which I assume is within it's capability and the op-amp basically reverses its polarity with respect to the same ground. You can do it using only resistors if you are very careful by balancing a positive output from the PLC card against the negative voltage supply but the control will be reversed, that may be something you can work around in the PLC control program.
Brian.