Play PCM stored in EEPROM without microcontroller
This could be a fun thing to do and an interesting challenge.  It isn't likely to be the lowest power way of doing it though.  There are a lot of low power micros available.  

What you need, one way or another, is an address generator.  You could do this with old style logic or a micro.  Generating the address is the job that the micro is doing.  You could also use a cpld, but this isn't likely to save you any power compared to a low power micro either. 

Your system will need a clock and a micro may well include one.  This will save you yet more components and power compared to discrete components.