In need of a lightweight power source

I'd like suggestions on a lightweight portable power source for use in a wearable project. I have a top hat with 88 neopixel LED lights on it and a ~200g 10,000 mAh usb battery pack powering it, which makes things a little bit large, heavy, and unwieldy. I'd like something new. I think that anything upwards of 5,000 mAh would be enough power to get through a good long night with it on. Does anyone have suggestions on something lightweight I can use in this capacity range? Another smaller USB pack would be ideal I think, but I'm also considering some 18650 batteries. Two big 3000 mAh batteries in parallel would be ~100g and have more than enough capacity, but it would run at 3.7V while my Arduino Nano board is supposed to run at 5V. Would this cause problems? I know the lights will be dimmer at 3.7V but that's not too big an issue. I suppose I would also need protection circuitry if I went this route? Any other suggestions are welcome. Thank you!

88 x 0.06A if on full white = 5.28A.
Neopixels need 5V to operate, not 3.3V. Datasheet suggests 3.5V minimum.
Run for an hour = 5280mAH battery is needed.

Suggest running your code with a current meter and get a feel for how many mA it uses in actual operation.

WS2812B preliminaryV2.0.pdf (265 KB)