Power: (2) 3V lithium 123 batteries
Not sure that's a good choice. According to the ws2812b data sheet, the supply voltage should be 3.5~5.3V. If your batteries are in series, the voltage will be too high. If in parallel, the voltage will be too low. The voltage range for the tiny85 is 2.7-5.5V, so the batteries in series will be too high for the MCU also.A better choice would be a li-ion battery such as 18650 size, because it's rechargeable and because it's voltage is nominally 3.7V (4.2V fully charged and down to about 2.8-3.2V discharged).Another better option would be 3xAA NiMh rechargeables.
The resistor is not necessary ifThe LED strip is connected directly to the Arduino andThe LED strip is connected to the same 5 V power supply as the Arduino at the "5V" pin.Note that the diagram above is misleading! It incorrectly shows the black (ground) wire going from the power supply connector to the Arduino.The ground (black) wire must run together with the green (data in) wire from the Arduino to the LED strip.Similarly the capacitor must connect directly at the LED strip and the resistor should be located there at the LED strip rather than anywhere else.
This is a project I am looking to produce, so disposable batteries are definitely the goal here. What is your opinion on running the (2) 3V's in sequence with a diode, such as the 1n4004
You can use a buck converter to go from 6v to 5v, lots on eBay.A dirty way way is to add a silicon diode (.7 volt drop). You will need to watch load currents.6v - .7 = 5.3v
This is 2019 and the planet is in serious trouble because of the way we humans treat it like a giant trash can. No-one should be promoting disposable batteries in my opinion.