I don't think there are any viable options as such. All wireless headphones have a transmitting base station too, which usually runs off some A/C power. Even if its not A/C, when there is wireless, there has to be some power for transmission. So a device with say atleast same bulk as Axim won't really help. Even then, your headset will have some batteries too and you don't like that again
Only possiblity which exists at the moment is bluetooth headsets. For one thing, you have to buy a BT transmitter for Axim too. Then you have to enable/hack for a headset profile, which usually is not part for PPCs. Eventually you will get some wireless voice and that at less than FM quality because BT bandwidth doesn't allow much.
Long story short, stop day dreaming

and learn to work with a small wire.
- Itanium