However, I don't know if the current from (for example) an iPad charger would be too much. I assume the charger would just output its maximum 2.1amps?
This is a common misunderstanding. All common power supplies, including the mains supply in a house, batteries, laptop supplies and USB supplies, have a rated output voltage, and they are near that voltage whatever load is taken from them, up to their maximum current rating.
For instance, a 2.1 A USB supply is rated at 5 V, and it's perfectly happy producing 5 V at 0 A with nothing plugged in, or any current at all up to 2.1 A. A device that is plugged in will take up to 2.1 A, but it could be anything between 0 and 2.1 A. A cell phone might take 1 A when charging the battery, and that would fall as the battery is charged. The voltage won't change much.
It's the same with the mains supply. The sockets here are rated at 230 V, 13 A, and I can get 230 V at them with no load, or 13 A, or anywhere in between. I can plug in a USB charger, which will take up to about 12 W from the socket, just 0.4 % of the maximum that the socket is rated to and it's all fine.
When changing a power supply all you usually need to do is get the voltage correct and the current rating of the power supply the same or larger than the rating of the load.