Looks like fun.
The non-light up bit of the wiring can be a conventional hookup wire with suitable insulation thickness. Since the voltage of the inverter is between 90V and 120V AC, any wire sold in Australia with a 240V AC rating will be fine. It's kinda hard to find wire with a lesser rating here, although there's lots of wire with no rating. Black outer would be best, so it doesn't show up in performance.
If you have longer segments of EL wire than you need, you might also double them up on part of the bow (e.g. two metres in four runs over 50cm), for extra brightness.
For child safety, have your elves check each bow before it is activated for a concert, to check for damage since it was last assembled.
Another idea is to assemble onto a thin strip of perspex, and attach with clips or wire ties before performance.
The performance you link to looks like they were using LEDs and not EL wire. In particular for the yellow bow; spots can be seen. You should be able to get more light flux from LEDs, at lower safer voltage. The performers had cables between their hand and their sleeve, but not on the floor, so there was some sort of power pack in a pocket.
Hope that helps!