From attempting to assist the OP in various previous threads for a few years;
He seems to use " e cig battery " to describe a power device/mod, either internal or external/removable cell, all shapes & forms stick, tube & box shape power devices, and actual batteries/cells. (18650, 20700, 21700 etc..)
So, I'd be willing to bet he's after suggestions for a new power device.
Geekvape Aegis Solo if you're looking for a small 18650 single cell power device.
But, if you're going to use 40w or above a two cell device will give substantially more between recharge cycle run time than a single 18650.
Maybe a Vandy Vape Jackaroo using a 21700. a single cell device that can have an advantage in run time over a single 18650 device depending on the 21700 cell you chose.