It's probably an unregulated supply (transformer, rectifier and, maybe, a filter cap). It is rated for a voltage and current. what that means is that it will deliver thqqt voltage at that current. When you measure it by just putting a DMM on the output with no other load, the voltage will be a fair amount higher. what you have to look at is the voltage under the specificed load.
It sounds like the switch doesn't do anything but I wouldn't worry too much about it if you are using a voltage regulator (like a 7812). I'f no VR, I'd look at the relay datasheet - if it can handle 15-18V, I'd not worry about it.
By the way, I've had problems with the one switchable wall wart I have. It seems flakey but may have been killed by my wall-wart eating PIC programmer. but that's a different tale...
Phil