Are the resistors correct?
No the resistors are not correct.
Could not read the description only the voltages.
Using the average voltages:
5.5V supply, 3.2Vf @ 20 mA = 115 Ω
5.5V supply, 2.0Vf @ 20 mA = 180 Ω
Source: LED Series Resistor Calculator
all the parts have to be at very low consumption and very small
66 vs 100
Why 5.5V? 3 AAA batteries is 4.5V.
3.3V, if available, will be more efficient.
You should use the brightest LEDs you can find.
The higher the mcd or lumen, the lower the current needed for the desired brightness.
Cannot read the specs on the LED you chose, but for example let's say the green is 100 mcd, 3.2V @ 20 mA.
There is a Cree C503B-GAS-CB0F0792 green LED, 5mm, 53,650 mcd @ 20 mA
To get 100 mcd out of the Cree LED. You would only need 100mcd/53,650mcd x 0.02A = 370 µA
That's 0.000851 watts 0.85 mW vs. 115 mW for 20 mA for a 13,529% less power.
Bottom line, use a bright LED at a lower current.
If you could use surface mount LED:
The brightest and smallest: Luxeon Color C Line
What microcontroller can I use
Atmel is always a good choice.
Here is an ATtiny85 from Adafruit Adafruit Trinket - Mini Microcontroller.
Uses Arduino IDE
Smaller and lighter than the Arduino Nano.
Nano: 45 * 20 * 3mm 6 grams
Trinket: 27 x 15 x 4mm 1.85 grams
I could not find a smaller lighter LED blinker circuit.
They do exist, just could not find one.
This PCB was a blinking LED for a Logitech mouse package.
The blinker circuit is under the block blob.
Side note: If you are using AAA alkaline batteries, you will do much better with the lithium. The lithium starts with 1.6V, and at 400 mA for 1 hour, holds the voltage above 1.4V. Where the 1.5V alkaline would drop to 1.2V.
If using Li-ion use Lithium Nickel Manganese (NMC) for highest power.