You can splice the wires together, they should go brown to black, and blue to white.... By following the pinout of the switch and the pinout of the wires that is the correct method for powering on this powersupply. I personally like to double check every hard-wire im going to make with a voltmeter that way I know what is being put out, and where. But that is just me, Im a nut....LOL
*-*-*On the other hand.*-*-*
You can go to radio shack (Etc.) and buy a replacement switch. They are super cheap, (A dollar or two.) and easy to install.... Here is the info just in case you want to go that route...
Switch Connection Instruction: The connection instruction and diagram should usually be printed on the power supply label. There should be a line dividing the four pins on the switch into two parts (P1 and P2). Connect the brown cable to Pin 1 (top-right as shown in picture) and the blue cable to Pin P1 (bottom-right as shown) on the same side. Connect the Black to Pin 2 (top-left) and the white (or red) cable to Pin P2 (bottom-left) on the same side.
You are correct in the assumption that the green/yellow wire is the ground.
Going with the second route you gain the ability to have a nice kill button in case you need it... Comes in handy sometimes especially when you dont want to get down and turn off the back of the powersupply, you can route this to normal hand level....
Good Luck!
XS