If you already have some cuts you want to smooth, you can brush the styrofoam with a paint brush dampened with acetone or finger nail polish remover. Don't use too much! Watch this to see why. Also use good ventilation which you can also find out why in this clip.
You can DIY your own smooth cutter with items you probably already have in your garage or trucnk of your car.
hey my buddy has what he calls a "wood cutter" says thats the name of it. basicly what it does is heats up a (whats the razor blades called that go in the little pen like handles? used for detailed cutting) anyway it heats up the razor blade and and it cuts threw strofoam like butter.
I think Xacto knives are what you are refering to.... We talked about several types of styrofoam cutters HERE.
Ni-Chrome wire has an internal resistance that causes it to heat with electricity applied similar to the element on an electric stove.