Unless you're really low on cash, I highly suggest buying
this Seasonic M12II 520W rather than screwing around with cutting wires. It solves three problems: reducing the chances of wires shorting causing a burn out (and/or a fire), reduces cable clutter (modular cables, just leave what you don't use unplugged and stored somewhere else), and replaces the shoddy PSU you're currently using with a quality unit.
If you need something a bit cheaper,
this Antec Basiq 550W is worth a look, though the Seasonic should be a much better platform.