Thank you gents, your input has been quite valuable. It confirms my fears, and I will get the appropriate battery.
Evey datasheet regarding 3400mAh Panasonic batteries I can find indicates that the maximum discharge rate should not exceed 2C (about 6.8A) regardless of the PCB cut off, and while this may work quite well for an in-hilt LED saber, it would not be fit for a neopixel blade. I will go with the high discharge (15A) cell instead.
Thanks again!
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