You may not have a problem at all. The OM2 has two separate metering systems. One measures through the prism and that is what you see in the finder. The second system measures the reflectance of the film. It all starts with an approximate shutter speed from the viewfinder , than when the mirror goes up,the lens diafragm closes down, the shutter opens and is then controlled by the sensors that measure reflectance. If there is no film in the camera, it will measure from the pressure plate which is black and so gives a much longer shutter time. It is a wonderful system that really works well, as long as you have a film in your camera.
The OM10 also works like that. Never use the automatic setting without a film in the camera. Of course, if you had a film in the camera, you might think of buying another (working) one.