Charger that lets you use an iPod Touch while charging?
I have an Apple USB Power Adapter that came with my iPhone and in no way does it prevent me from using any feature of my device while charging. I can play audio out of the built-in speaker as well as through the headphone jack without issue. I'm not sure what wall charger you have, but if it's the Apple USB Power Adapter you should try to return it or exchange it as yours is likely defective.