Ok to put peoples minds at rest, Ah listed on any battery is only a concern if there is not ENOUGH Ah to do the job for any real long period of time. So Big Ah numbers good (mostly, get to that later).
What's more important is a battery or batteries total potential VOLTS. That's whats going to do the most damage the quickest if its to high, why....well here comes the high Ah bit, if you have a incorrect Voltage with a high Ah rating its burns through components way faster than you can blink.
Remember, its the Volts that give the POTENTIAL Difference to commence work, but its the AMPS that do the work and a electrical/electronic device will only EVER draw as much current (amps) as it needs to do the job IF all is well with the device.
So think of it like this, Volts push/pull the amps that do the lifting, ok. (real rough but you get the idea)
Ergo, you want a long running session with your HC, then shove in the damned biggest Ah AA that you can find but for gods sake don't ever get a short !