You can use a normal wire in place of the muscle wire as I know it is not easy to get
I was planning to use a big potentiometer to possibly attenuate the current.
not a circuit diagram...I am not an electrical engineer
At 5V from the Arduino, I am only passing through about 240mA
The resistance is 20 ohms/meter or 1/2 ohm per in. I am using about 16" of wire so internal resistance of my wire is about 21 ohms.
The trick to working with a manageable current requirement with muscle wire + Arduino is to play with the duty cycle in your code: that is, playing with the HIGH/LOW duration.