You don't want to bend any of the fan blades or hit the radiator with the fan, so go easy with the prying or slip some cardboard in there to protect the radiator if it comes free suddenly.
I'm guessing you removed the 4 nuts that hold the fan clutch to the water pump shaft, not the 4 bolts that hold the fan to the clutch. You can remove those bolts once you have the fan and clutch out of the car. Did you get the fan shroud out of the way? It helps to have extra working space, although the fan shroud might not come out without removing the top hose from the radiator(creating more work and a mess).
If you can slip a long prybar, metal pipe, or even a broomstick between the fan clutch hub and the water pump, it afford you some leverage to get the clutch to let go of the water pump shaft, but watch what you use as the leverage point(dont damage the alternator or something else by carelessly prying away). Penetrating oil on the mounting flange can help here, too, since there is a nose on the water pump shaft that sticks into the hub of the fan clutch, and it can get rusted in place. Sand off any rust before putting the new clutch onto the water pump, and apply a dab of grease to prevent future rust.