Are all the feeds positive voltage, or are you using any of the feeds as a ground reference? In other words does your project have a negative supply rail?
Is this a TTL IC? Can you substitute a CMOS type? It draws less current and can use a range of supply voltages.
If you have 5V then you can get a 4.4V feed by inserting an inline diode.
Do you mean you want to prevent current flowing backwards through the battery when you use the wall adapter? A diode is the simplest way but it will subtract .6V when you draw from the battery.
Suppose you were to use a rechargeable 9V (the 8.4V type containing 7 cells, not the 7.2V with 6 cells)? It could charge at 9V from the wall adapter. No intervening components will be necessary.
Each cell would be maintained at 1.28V which is about the same as its voltage on a shelf.