I did not fully understand what you want to achieve. The maximum current rating for an Arduino chip is 200mA. Not for one output, this is for the while chip. The outputs can source at most 40 (or maybe 50) mA.
Since your wires have ~1 Ohm you would get more something like 4-5 A from a 5 V source. So this is far away from what an Arduino can source. You need to consider some Transistor in between to amplify the current.
Udo