Okay, I am going to be a little tough on you. Don't be offended, but YOU elected to raise chickens. Take the good, the bad and all the responsibility that comes with it. Just do the dirty deed and be done with it. The poor chick is probably suffering as you try to figure out a way to make this easy on yourself. Freezing is cruel. I have to believe the little gas bag method is no less than suffocation. Off with the head. Plain and simple. Cervical dislocation is fine if you know what you are doing, but let's be honest: you don't want to do this and that's going to make you use less force than necessary. You will probably just sprain its neck. Plus, with a chick that young, it's too difficult to gauge the force. There is a very fine line between enough force to dislocate the vertebrae and enough to pop its head off. Which brings me to my preferred method. A day old chick is most easily dispatched by popping its head off. That's right, city chicken farmers, it will come off easily in your hand. Just like game bird hunters do in the field when they retrieve their doves or quail. Larger birds, they dislocate the vertebrae. If that's too difficult, snip it off with a pair of scissors. Just be sure not squeeze down until the scissors are in place (and your fingers are out of the way) and then snip quick and hard. As they get older, pulling the head off gets a little harder and messier, but under a week or so, it's quick and easy and not that much blood.
Please don't take this the wrong way. I don't mean to be insensitive. Nobody likes doing this. But, part of the due diligence in deciding if raising chickens is right for you is more than just determining you have the room and like eggs. You have to be prepared to cull and euthanize when necessary and do it quickly and effectively. If you can't check that off your list, either because you are willing or have somebody around at all times that is, you shouldn't get chickens.
Good luck to you.
UGCM