I was thinking about getting a cable for Pi Zero, this one: https://www.adafruit.com/products/1995
But it's 2.4 ampere, won't that overcharge the little Pi Zero and damage it?
The specifications say that: DC OUTPUT VOLTAGE RANGE MAX 5.36V (+/- 5%)
And the 5% extra is a bit worrying that is already 5.628 V, whereas the maximum tolerance of the Pi Zero is 6 volts, according to the website. That is very close.
So is it safe to use that power supply with Pi Zero, or should I just use the 1 Ampere official power supply?