Where to put the switch on a power supply? 5V/12V or 230V?
No you should not switch the +5/+12/-12 V lines as they're not switched now so switching them can cause unpredictable results.

If the system has a push button to power it down, use that and then disconnect the power at the mains (230 V AC) side. Using the push button informs the system to prepare for shutdown. This is similar to how a desktop PC should be fully powered down.

If the system has no way to power it down other than pulling the mains plug then obviously it must be designed to handle that. Then you can safely add a switch on the 230 V AC side. When the console is moved, serviced or there is a mains power interruption then the mains will also "suddenly" disappear right? Adding a mains switch is the same from the console's point of view.

Do make sure you use a switch with the proper voltage and current rating and make sure the user cannot touch the wires carrying mains voltage.