Essentially resistor values are for setting input impedance and gain, supply voltage has no bearing on it.
Where supply voltage does matter (and a LOT) is in the headroom - only a 9.6V supply is really pretty low and limiting. For a portable system at least +/-9.6V would be better, but usually either +/12V or +/-15V is used.
If the supply voltage is too low, then (assuming you pick opamps that will work that low!) you are seriously limited in signal and output levels, which in turn makes it all a lot noisier.