Pomona makes test lead wires rated at 10kV and more; this is what I used in the past for similar applications.
Here is how I spliced it:
- make a smooth solder joint with no sharp edges;
- smear some silicone sealant over the wires;
- put a heat shrink tube over it;
- another layer of silicone;
- another heat shrink tube.
You can shrink the tube right over uncured silicone. The excess will squeeze out.