Can I use this power supply with my Arduino?
Yes, that power supply is ideal for powering an Arduino (an Arduino doesn't care if it's linear or switching, and a linear regulator that goes from 220V to 5V is called a furnace, and you don't want one of those...)

HOWEVER unless you have a very strange wiring setup in your house, under normal circumstances there is no 220V supply in the switch.  You normally have live in, switched live out and NO neutral connection.

That means you don't have the connections you need to wire your power supply up to.

By the way: if you didn't already know that then you are not qualified to mess around with home wiring and you should leave it to the professionals.