Battery Power Supply Yes_ or No_

It seems to me that a phono stage is at a greater risk to noise than any other gismo in a system.  Mine makes a slight hum, and I am considering saying "la byby" to it.  Some years ago Sutherland sold a phono stage that was battery powered.  The theory being that this arrangement would substantially lower the noise floor.  I am considering a Project phono stage that uses a 18 volt wall wort for a power supply.  It is a metaphysical certainty that some noise will creep up that power cable.  So my concept is to wire 3 small industrial 6 volt batteries together, such that they produce 18 volts, and chuck the wall wort..  I think most people who post here are further down the knowledge trail than I am.  I hope some of you will share your wisdom regarding the above.  Gratzi, in advance for your thoughts.