Stan,
Consider using Dawn instead of Simple Green as the latter reportedly can attack aluminum if left on for an extended time. Regardless of what you use rinse it off before it drys. Unless radiator is super dirty, you should be able to clean it without removing fan. If it is super dirty, consider having it steam cleaned, especially if it has oil and grease residue. Use a hose, not a pressure washer as its force can/will bend the fins.
Steve