Hi,
I'm translating some Tai Chi ex into English and her are some of the description which involve description of circular movement of the arms:
With your arms in front of your chest and slightly bend, swirl your left arm from below like drawing a circle.
Your left hand should reach the level of your shoulder at the end of the first half of the circle and you should be able to see your left hand by turning your body slightly to the left.
Then continue to swirl you left arm back to the front while turning your body to the front again.
I would simply use "move" -- especially since you've described the circular motion: I don't think you don't need a verb that adds to the description you already have.
I'm still a fan of move. There may be a better word, but swirl isn't it, in my opinion. If I were writing it and wanted that circular description on the backward motion, I would say, Move your arm backward in an arc and then push forward.