Doesnt sound like you want Hot wire . .. that would be more for free-forming, and cutting thick stuff.
If you want to "cookie-cutter" a bunch of "parts" then steel-rule is the way to go.
'll suggest that you find some .030-.060 thick steel for the die.If you try to count on thin stuff holding-up, you'll be pissed when it folds on ya. . .(AND have with a sharpened edge. . .why cut with a dull knife)
You'll want the heavier walled steel for thicker (taller) material, and/or big lazy profiles. (flexable foam is compresses to "thin' when cut) If, otoh, you have tight countours, the thinner steel can utilize the support of the tight folds (and be okay).
maybe search under steel rule die
stock for base materials.
http://www.schroederinc.com/materials/