You can build a larger hot-wire cutter really easily.
You'll need some scrap lumber, a length of NiChrome wire (although .025 safety wire will work in a pinch), a small tension spring and a model train transformer (Lionel works great) wire, alligator clips
Build a U-shaped frame out of 1X2 big enough for whatever you're going to cut. Attach one end of your wire to a nail or screw on one side - attach the other end to the spring and attach the spring to the opposite side of your frame, making sure the spring keeps the wire very taut. Connect one lead from the transformer to the fixed end of the wire. The other lead goes to an alligator clip.
By adjusting the location of the second clip (ie. the heated length of wire) and the 'speed' on the transformer you have wide latitude in adjusting the temperature of the wire - which determines speed of cut and indirectly smoothness and accuracy of cut.
I'm not making it up as I go along, I'm establishing precedent