the long cord and connector bounce around a lot

A 3.5mm stereo plug and socket, a piece of light coax cut to exactly the right length for your body and ten minutes with a soldering iron will sort that one.
Oh, and before you solder the second end, thread the coax through the hole in a perfectly ordinary small stationery crocodile clip and knot it, to attach to your jogging kit.
- from Mrs. Beaton's how to listen to Mp3's!