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Generally a heater polarity isn't of much concern if it's just straight 2 core wire. Though if you have a multimeter available you could check the polarity. If it's only using barrel jacks convention is centre positive on output jacks though I do have a few I ordered which I'd tested before use and found reversed connections one end (small extensions with 90 degree plug one end). Though they come in handy at times playing with small DC motors, switch extension cable in to reverse motor.
The resistance for the element should be within the element (nichrome wire or resistor band (maybe that's just my home made thing) not in the cable and cutting it should make no difference to supply.
In saying this I'm not familiar with the ASIair and what it has.
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