Power consumption NeoPixels vs. direct control?
There's certainly truth in the WS2811 having a non-negligible stand-by current. You could, however, rather easily remedy that with a high-side switch that only powers the IC when needed.

Then, while PWM certainly is cleverer in perceived brightness per Joule than adjusting the sunk current, you still mustn't ignore the fact that this is essentially a linear power supply for each LED - all the difference between LED forward voltage (at the 18.5 mA that the WS2811 tends to sink) and the supply voltage will be converted to heat. So, if your LED forward was e.g. 2V, and your battery is a 6V source (2× CE2032=3V+3V), you'll get an efficiency of only 33%, as two thirds of the voltage are dropped over the regulator.

In that case, using a switch-mode step-down (voltage) converter to get the supply voltage down to close to the minimum necessary voltage would work better here. One could then argue that if you can do that in the first place, simply having a switch-mode constant current supply that can be en- and disabled with a PWM would even safe the energy for the WS2811; but considering you're still driving a full set of LEDs at 18.5 mA, that 1 or 2 mA wasted is peanuts.

By the way, your CR2032 are definitely not meant to source currents up to ~60 mA; you'll probably see that during high-load times, the battery voltage drops below 4V.

And: an Arduino isn't the most power-saving choice, either, especially not with the 5V-based Atmega MCUs. I'd recommend going for one of the ARM-based arduinos. Especially the STM32Lxxx ("L" like low-power) series would be a good choice. Then again, the Arduino environment itself isn't meant for very low-power designs (making it hard to impossible to use lower-power modes) and energy-efficiently addressing the WS2811 (where you'd want a series of automated DMA transfers to happen while the CPU sleeps rather than using the CPU in idle loops to bitbang out the WS2811 "protocol").

Detailed information on how to save energy in your overall design, however, would require a different question with a different background – I think we'd all like to advise you if you can ask based on a project description including a schematic!