Running AAA NiHm for e-cigs you will very likely be better off running 5 batteries and using higher voltes and higher resistance devices that don't require as much current. At higher voltage you can get about 8.5 watts. You would need about 2c current and even the 800 mAh eneloops will do the job quite well.
If you like things hotter and need more watts you will likely need to move up to AA which can deliver about 150% more current then AAA. You can run just about anything with that including LR and a true regulated 3.7v and the AA NiHm won't even break a sweat.
LS-D NiHm batteries like the eneloops (the reason I mention them is because they where the first on the market to use Low Self Discharge and are what I am familiar with. Others have come on the market since they appeared but I haven't kept up with the market) are noted for putting out consistent voltage throughout the charge which make them a good choice for high demand e-cigs.
The puck looks interesting, but as mentioned, I think 5 AAA with VV would be a much better choice as it gives the option of using HR. That would be a good deal easier on the current load. With AA four would be plenty.
