The best solution that I can see would be to buy a small mp3 player that suits your music needs and then trawl your local outdoor recreation place for a suitable waterproof enclosure - you will usually find a selection with the canoeing and kayaking gear. It wouldn't take long to modify it to allow the headphone cord to pass through. (Drill and silicone sealer would do a permanent job).
If your mp3 player is as small as a packet of cigarettes then you are golden. That size is somewhat easy to find.

The only downside to this is that you will have no way of controlling the player when the case is closed. I don't know how much of an issue that is for you.