It depends on if you have a 2- blade or 4-blade fan. if you have a 4-blade ( unless the blades are bolt on) you will have to remove the radiator. I have actually done it once with a radiator on but that's another story. If it's a stock 2-blade fan ( original or repro alum) you can/should be able to remove with the radiator on. You can try first with the hoses/radiator in place. Remove the 4-nuts and pull out and up with the fan and water pump toward the upper tank. If there's not enough clearance I would try pulling the radiator forward. Loosen the front nuts holding the hood rods to the radiator, slip out and place down below radiator mount bracket , and then with some help get the hood off unless it's already off.
loosen upper radiator hose clamps, make sure hose is free and have someone pull radiator forward at the top. This is assuming you have the correct spring mounts on the radiator. I have done this numerous times with success.
Most of the time it will give you more room to remove the pump and fan on a 2-blade. As I said before, in many cases you don't have to do this... but if there's not enough clearance it gives you the extra little bit. It's absolutely NOT necessary to remove a headlight bar and headlights to remove a radiator. You don't know what you're getting into in doing that on some cars. Also, no need for the newfangled studnut combos. If you have the original studs on fine. The do not effect the clearance. It's the impeller that's the issue with that, not the studs. I've never removed one that the studs were the problem.
Best of luck,
Larry S