Sure, but we don't get to choose how much current goes into the battery. The charge logic in the device (any device that has a built-in Li-ion or similar battery) controls and monitors the charge process, this is the only way the batteries can be charged safely, efficiently and with predictable results.
Our job is simply to provide a source of electrical energy in the correct voltage range for the charge logic to operate, and with sufficient ability to deliver the current required for charging the battery.
If the power adapter we use is beefier than required then either of two things can happen:
- the charging circuitry can make use of the extra power and charge the battery faster (but still withing safe specs)
- the charging logic will draw the same current as with the standard charger, and we've wasted our money
If the power adapter is underspec'ed (e.g. a computer USB port) then either of these two things can happen:
- the power adapter can get damaged (unlikely, because they are usually designed to protect themselves from excess current draw)
- the charge logic recognises the reduced ability of the power adapter (either through communication with it or by monitoring the supplied voltage, which will drop), in this case charging of the battery will simply take longer.
There is no danger of damaging or harming the battery in devices like the watch or the iPhone,
as long as one provides the correct voltage (5V in this case).