Edit: Hold on, wait.
Normally 8 AA batteries equals 12 volts DC. But looking at the parts involved, it's possible the batteries are in series-parallel. I would reassemble it as-supplied, put the 8 batteries in, and measure what's coming off the end of the batteries.
If it's 12 volts (all batteries in series) nothing easier. Dive into your shoebox of old wall-wart power supplies. One of them is bound to be 12 volts DC, since that is the most common voltage. Hack off the wires... or if you want to retain it for its original use, visit Radio Shack for a socket compatible with the plug (the 12V DC ones are fairly standard). These can also be bought new if you never save them, or ask your friends or neighbors if they have any.
If it's 6 volts (2 parallel strings of 4 each), you can use a common wall-wart that is 6 volts instead of 12. These are far less common, but you can buy new ones. But try this: test the product again, only use NiCd or NiMH AA batteries. These cells are 1.2 to 1.25 volts per cell, or in a stack, 4.8 to 5 volts. Exactly the voltage of USB! So if the charger and drone work normally and to spec on NiMH/NiCD batteries, they should adopt straightaway to USB charging. I would use a 2A supply like an iPad charger, and not a computer port.
The general concept here is to supply power in a way which emulates and replaces the AA batteries, and do not tamper in any way with the factory as-designed circuitry which is responsible for safely charging a lithium battery.