You will get cold water if it's from the mains ,which it almost certainly is. You get hot water from your baths hot tap because it's much lower than the little cold water tank that is sitting above the hot water cylinder ( it's integral ,looks like part of the cylinder). Once you start to raise the hot outlet ,the pressure drops. Judging by the measurements you gave ,your shower outlet will be virtually higher than the hot water cylinders top ,and pressure will be zilch !!