Is it safe to stick an Apple Watch charger to a piece of metal when not in use?
The short answer is you are safe as long as the ambient temperature and charge hardware don't overheat.

The empirical evidence is you can measure the temperature of the wall adapter and the charging puck to approximate the amount of current that's flowing through the inductive charger at any point in time.

I like to use a fancy infrared thermometer for things like this, but you can use your fingers to know that the charger is within specifications by comparing the temperature change when you take a charging watch off the charger and then let the charger sit against your chosen piece of metal.

Apple's official safety information are at:


https://help.apple.com/watch/ or http://manuals.info.apple.com/en_US/apple_watch_user_guide.pdf
https://manuals.info.apple.com/MANUALS/1000/MA1712/en_US/Apple_Watch_Info.pdf