I have a fairly large variable powersupply, but I'm sure a train regulator can be used if it can handle the current.
You can use thin piano wire instead of nichrome. I got a length of nichrome wire from a fellow modeller years ago and it is still in use. With a 12volt battery current draw is app. 4 amps and this gives a good temperature for cutting so a PSU is not really necessary.
HWC is NOT a black art although many people seem to think so. I have built several foam models where templates were used to cut fuselage parts - see the Hellcat and GeeBee on my homepage: http://fly.to/epilot