What ISS does to dump heat is not usable for a reactor
Quote: If I'm not mistaken, they already use radiators on the ISS.
Yes they do (ammonia as a working fluid if memory serves me right), but for nothing anywhere near the amount of heat which is dissipated by a nuclear reactor. They also (ab)use the fact that the station is reasonably reflective and heat insulated by orienting it so that the radiator is in the shade thrown by the station.
The surface area of a purely radiation cooling radiator which operates in the "boiling water coolant" temperature ranges typical for modern nuclear reactors will be enormous. You cannot hide that easily in the "spaceship shade". It will be too bloody big.
The only solution is to increase the operating temperature so your heat transfer rate per m^2 is higher and thus decrease the radiator size. Getting that done and combining it successfully with a nuclear power generation cycle is a non-trivial engineering problem.