Is it possible to remove the cooling radiator from a 1999 Eddie Bauer without also having to remove the cooling condenser?

Yes , but please take no that the bypass system allows the coolant to keep moving through the engine to balance the temperature and avoid hot spots. Because flow to the radiator is blocked, the engine will reach operating temperature sooner and, on a cold day, will allow the heater to begin supplying hot air to the interior more quickly.