Hi you should be able to remove it without the bumper removal, take away the plastic cover trim that sits on the front by the top of the bumper that should expose the top of the rad, undo the securing bolts and lift upwards the bottom of the rad normally has a pin either end that locates into rubber mounts on the H frame at the front, I would advise buying a new top and bottom hose as in view of the cars age you may well have to cut the hoses to get the rad out, the hoses are well known to almost weld themselves on to the connection pipes on the rad.
Steve.