bro the wires going from the socket to the ballest have nothing to do with 220 or 110 you will have no problem extending them if it was either way.you can use any wire that is 14 gauge but does not limit you to 14 as long as its not smaller then that it will be dine i personally strip an extention cord and take out the black and white cords this way it moves easier.My light had 3 wires going from the ballest to socket or bulb.1 green 1 blue 1white i took the green off this was the ground wire but my ballest was already grounded and i know there is no problems there.you then cut the wires and extend them dont be scared be sure to use wire nuts or electric tape or crimps on all your connections the heat that will be removed is worth the risk and i'm telling you i've been wireing since i was 15 its pretty simple if you keep it simple



p.s. there is nothing wrong or diffrent because the one wire is bigger its just your neutral wire other wise known as a common and does not haft to be bigger trust me good luck