NiMh AAs can handle the current. Unless we are talking about some lights like the not-exactly-small Zebralight SC5 that reaches 500lm on an Eneloop Pro, pushing them close to their maximum, the limit would be the small boost driver that increases voltage from 1.x V to the 3.x V used by the led. The best 14500 at the moment would be the Vapcell 14500 that has a capacity between 950mAh and 1000mAh.