Many wall-wart adapters give higher voltages with less load. You have to match the voltage at a rated load. That is, if using only 100mA on battery, and you try to use a 9V 600mA wall-wart, its voltage may still be high like 12-13V at a low load level. That 600mA wall-wart will give 9V only at 600mA
That said, there are some "switcher" types of wall-wart adapters, and those are steady voltage regardless of load. You have to measure the voltages carefully while plugged in.
Another option is to build in a small 9V regulator circuit (3 parts), and feed it from the 15V charger. Since it won't be charging without batteries installed, you can simply run the device off the 15V wall-wart with a 9V linear regulator chip (LM7809)