You mentioned that you have the stock cable going into a 3.5mm converter? Do you mean you have the 6.3mm end going into a 3.5mm adapter so it will fit into the dongle? Because the stock cable is a 2.5mm to 3.5mm with a 6.3mm jack adapter on the end of it that can be unscrewed.

Regarding the cable itself, you could get a velcro tie and wrap up the excess wire to have it look cleaner and be easier to carry around. It's what I'm currently doing with my pair.