Removing ripple in DC supply
In your job the current is low and the DC voltage does not have to be at all    accurate .Batteries themselves however do not make ripple which means that the ripple rejection of your preamp may be poor .Single ended discrete component circuits can have poor ripple rejection but they sound good .So keep the adapter and the preamp and place some RC filtering in the DC rail between the adapter and the preamp .You could start with say 47ohms and 2200microfarad 25V.This will reduce the power supply hum much better than capacitance alone.