Yeah that could work as well but im not 100% sure. Cause i dont know if its just like a normal SATA Cable. If you look at the Picture i made
you can see one side is the normale Sata Cable side the right one which is completely black. The brown one is the thing you need cause the internal connector in the PS3 is just a normal Sata Connector and not the one you have on the SATA HDD.
You have to have a Cable with a Male and a Female Connector.
The one with the golden thingy is the Male Adapter. The other one is the female one. In your PS3 you have a Female Adapter and most normal SATA Cables have two Female Adapters.