You need to use the green wire every time you connect the controller to the battery if you want to avoid a spark. If you change batteries (unless it's from Cellman), it is unlikely that it will have an incorporated spark-suppression resistor and you'll need to install one. It can either be on the battery leads or the controller leads, it doesn't matter. What does matter is that the FIRST connection between the battery and controller is through the resistor, followed by the main power leads.
It's not a good idea to leave the resistor connected because if something untoward happens in the controller or motor or their connections, you could get a large current through the resistor and burn it up. If it's installed inside the battery like the Cellman, you will have to open up the battery to make repairs.
Many riders construct a separate 3-wire cable with the resistor installed: Red = power positive, black = power negative, and green = resistor.