Type of wire for high voltage applications
Since your question isn't getting much attention, I'm going to go ahead and expand my comments into an answer.

You need a type of wire rated for high voltage.  Temperature doesn't seem to be important, but flexibility is.

The correct thing to use would be silicone insulated wire rated to higher than your expected voltage.  Like this stuff, for example.

That's just an example.  You can get it in different ratings and sizes from various manufacturers and sources.

An alternative for hobbyists would be automotive sparkplug wire.

It can be bought by the meter (or foot) at automotive parts stores, or (maybe if you ask nice) from automotive repair shops.

If you don't need long pieces, you can scrounge used sparkplug cables from the junkyard (or ask a repair shop.)  

Most sparkplug wires are of the "resistor" type.  I seem to remember that you are working on some kind of electric "joy buzzer" gizmo, so resistor wire may be a good thing.

Resistor sparkplug wire has one down side, though.  You cannot solder it.  

You will need to use the crimp on brass connectors.  You can solder to the brass parts after they are crimped on.

If you repurpose used spark plug wires, you will usually have a connector at each end.  

If you buy new sparkplug wire, you can try to get wire core (like I linked to) rather than the resistor wire you will find in used sparkplug wires.  You can solder that rather than using the crimp on connectors.

If you try to buy new sparkplug wire, and can only get resistor sparkplug wire, then you will need some connectors.  Buy them where you buy the wire (or scrounge some old wires and pull the connectors out.)



Resistor sparkplug wires don't really contain what you would think of as wire.

It uses a string that is impregnated with carbon.  This gives it a high innate (built in) resistance without having a seperate resistor.

They use this stuff because it causes less radio interference when the sparkplugs fire.