You can definitely remove the water pump with the radiator installed.

Get some cardboard and tape it to the inside of the radiator to save your knuckles.

Also, you'll need a 10mm box wrench that's modified on the nose to make it a bit thinner. Don't try and remove the four screws that hold the fan in place with an open end wrench. You'll just put yourself in a world of hurt when they round off.