I did some more surfing ... uhhh, research, yeah that's the thing, research ... on rechargeable batteries, mostly looking at D cells.
First item - most NiMH D-cells are actually AA cells in a fat empty jacket. A real NiMH D cell will have 9000 or 10000 mAh capacity, and will probably cost $10-$15 each.
Second item - you can't buy a good charger for a real NiMH D cell, even when you can find the battery itself. All the good chargers use the "negative delta V" method to detect when the battery is charged - the voltage actually drops slightly at full charge. This effect disappears at slow charging, and works best at the 1-hour charge rate. That would be 9 or 10 amps for a real NiMH D cell, and few chargers provide more than one amp.
Since the smart chargers are not smart with real D cells, you wind up charging at some form of slow charge or even trickle charge rate, which means you have to monitor the time on charge, be sure the cell is actually depleted before charging, and you'll still get less than optimal life from the cell. The alternative is to get the cheap fake D cells, which will give maybe 24 hours per charge in a Quickie.
Third item, most of the available 9-v chargers are not smart chargers even if they are "smart" when charging AA and AAA cells.
Now you would think that a trickle charger would work for both, if it charged the batteries whenever the Quickie was off. So, what's a "trickle charge" rate that would be safe for the battery if left on indefinitely? Turns out there's not much agreement on that. The traditional rate is C/10 (one tenth of the 1-hour capacity) but NiMh cells are less tolerant. One source recommends not exceeding C/20, but only if you limit that to 20 hours maximum. Duracell recommends C/300 "to compensate for self-discharge" and it's not clear whether that would actually charge a cell or just maintain its existing charge. The C/300 rate would at best permit 4-5 hours a day of operation, since battery life is not quite 100 hours with NiMH batteries.