A lot of women mistakingly think that they can't do arm exercises or lift weights because they will bulk up like a classic chunkhead. But this logic is extremely false. If you're trying to lose weight, muscle burns more calories per unit than fat, which means gaining muscle is to your advantage.
Additionally, lifting light weights (2-5 pounds) will make you gain lean, long muscle rather than the thick ones you see on guys who lift weights.
So if you want long, lean arms sans the side arm flaps, then check out this video for arm exercises tailored to women.