It handles fairly well in the wind and i usually carry my paddle in my other hand but as the person has mentioned above you can put it under the bungie, i prefer to have it in my hand.
Yeah it is currently a bit bulky but as i am making it for a design project at school it is just a prototype. i store it under then bungie when i ski, i dont leave it at the beach, you can just wrap the strapping around the padding and put it underneath.