That looks like a light that I really want to add to my already too big collection. Thanks for the info. Now I'll try to answer your question.
A lot depends on what that 4xAA holder does with the 4 AA's. There are only three possibilities, 4P, 4S or 2P 2S. Since the output is different using 1D or 4AA's. I doubt it's a 4P configuration because the voltage is the same 1.5V so the light would need some type of mechanism to detect the presence of the holder like a magnet, mechanical switch or whatever. So 4P won't help you if you want to use an 18650, too much voltage. 2P 2S you might also have the same problem, even if you use 4 brand new lithium primaries. That would be about 3.6V in a 2P 2S configuration, depending on the driver voltage range, with an 18650 you might pop it or you might not. However I do believe you have the best shot with 2P 2S 3.6V vs. 4.2V is often within tolerance. If it's 4S then for sure the driver won't pop but who knows what the output will be, it's ready for 7.2V but you are only giving it 4.2V.
Frank