It really is easier just to take the 20 or 30 little screws out of the back of the keyboard, pull the metal plate, and gently put the membrane aside (fragile things.) All the keys will stay on the keyboard, and you won't have to worry about springs flying everywhere. If it is dirty enough to require all the keys be removed, it's easier to pull the keys apart from behind with a pair of pliers anyway.
Just my experience, and I've stripped a few keyboards.