Cleat problem, stuck in a shoe
Do you mean it's stuck? It might not be that you've got the wrong shoe in the pedal but that it's rather stiff (the pedals seem to arrive at up with tight springs) and holding it in your hands you can't get much force. The actual cleat is symmetrical. Try putting a crank arm (or whole bike) on the pedal, and putting your foot in the shoe, then twist your foot, holding the crank or bike. It should just pop out as if it was the correct shoe. 

I've got walkable SPD shoes and pedals with a cage round the SPD, which means more to get in the way. But when first setting up the cleat tension I though this would be a good idea. It's a good lesson in how much stronger your legs are than your arms.