Here's a quick way to keep your messenger bag strap from swinging around. The metal handle on mine would always be swinging around, hitting my bike, bike buckle, or smacking me in the hand. Here's a video of it in action:
Apologies for not taking photos along the way, but included here are photos of how the magnets are now taped on. I used cheap ceramic magnets, but you could probably use stronger ones have have this be much lighter. One important note is to make sure all your magnets are aligned correctly before taping. You want them to stick, of course!