I have used a 240v (Aust.) to 24 v transformer used in low voltage hvac controls connected to nichrome resistance wire, ran the wire through a hole in my steel bench up to a spring hanging from wood fixed to the shelf above. Alligator clips from tx to cutter wire, one connected under the bench and the top one on the wire can slide up and down to vary the resistance and therefore the heat. You will fiddle a bit to get the tension and heat as you need.
You can find resistance wire in old heater elements or rotary style variable resistors. some electronics shops will sell it in small packets.
If a wire cutter dosen't work you could try an old electric bread knife.