Is it safe to do? I heard that the PS3 had some major issues with overheating which often lead to the so called "Yellow Light of Death".
It should be safe, that was related to improper cooling of the main processors, not the power supply.
OP if your ps3 still turns on I would snoop around while its running to try and figure out what the PSU module is looking for in terms of a turn on signal. Its really likely that there is a standby rail that runs all the time, and a main rail that comes on when the PSU is activated. If I had to guess you can probably get it to turn on by connecting two wires together. Optionally you can get an xbox 360 power brick for very cheap and those have a known pinout.