I do not think the manner in which you swing your arms makes much of a difference. If you watch the video on air squats on the main site they actually playfully go over different "forms" that people do, one of which being called the "swimmer" i think?
One thing I would comment on though is the fact that your arms are so low at the bottom of your squat, that is going to predispose you to curving your back at the bottom. When you swing your arms out in front they should be pointing up and away, not down in front of you. By keeping your arms up you pull your chest up and force a good lumbar curve which we all know is paramount in good squats
Hope that helps!