Hacking the radio supply would able you to have an excellent stabilized generator, for 11-12 volts, or 6 volts, if you continue to use the clock in the same time.
In the radio, the voltage supply, is composed by :
This system is called "Output Smoothing" : principle : http://en.wikipedia.org/wiki/Image:Diode_bridge_smoothing.svg
The transformer supply 9 or 12 volts in AC, and the diode bridge transform it into DC, but there is always "variations" of current, then there is a capacitator to avoid this problem and have a stable DC.
A generator like this cost, approximately 20 â¬ -16 $ in an electronic store.