Its going to have to be a combination of diet and exercise.
You can't chose where to lose the weight... But if thats one of the main areas the fat is gathering then when you slim down that area will thin out as well. So the first thing I'd say is clean up your diet- clean eating, lots of water consumption. And next exercise...I know you are saying you don't want muscles (I'm not sure why not) but as you slim down you are going to want your skin to tighten/tone with you. That's where the exercise comes into play. Muscles don't happen overnight but just some full body exercises will work all of you and tighten/tone everything as you lose weight, including your arms.