I have been absent from the forum for a long time, and have not constructed many sabers, but I wanted to get back into it and found a new world of technologies, quite frankly, overwhelming.
So I find myself in need of advice from those more knowledgeable in electronics.
I am trying to put together a Neopixel blade driven by a CrystalFocus X board. My concern is with the power draw, and what battery pack is the appropriate power source.
If I understand correctly from reading about Li-ion batteries, there is an inverse relationship between the battery capacity (mAh) and the maximum safe power drawn from it. In other words, if I want to draw a lot of current (Amps), then I have to go to lower capacity batteries. My calculation of what a 288 pixels blade will draw puts me at about 4+ Amps, plus the power drawn by the board and the speaker. I have purchased Tim's Panasonic 7.4v Li-ion 3400mAh 18650 Battery Pack, but I am now questioning the wisdom of using this power pack with my setup, and wonder if I should go with the 1400mAh pack instead.

Can any knowledgeable electronics expert help me with this, please?
Thank you kindly.