Are you connecting the 2 3.7V batteriies in series to make 7.4V that you will then regulate down to 5V?
64 LEDS, if all on full at 20mA each, need 64 * 3 * .02 = 3.84A.
#2111, maybe 2110 if you bring the current down to 18mA
would be your 2 choices here
I can't open e-bay from here, so I have no comment on the item fungus showed.