I think if I were designing it, I would make the design suitable for burying in a hole, with a radiator that was positioned in such a way that it could be repaired without being directly in the beam of radiation coming out of that hole, or at least put a shield in the hole mouth. When the fissionable fuel was exhausted, I would want to bury the dead core in such a way that it would not leave much of a no-go area, so that a new reactor could be installed and hooked up in the future in roughly the same area.
So, this would be like simply burying the radioactive waste and reactor together when it is past its useful life. Assuming no water or atmosphere to cause metal corrosion and eventual release of radioactive materials (as would happen here on Earth), that might be a solution for radioactive waste on our moon.
But, I do wonder about the unintended consequences. For example, if we intentionally locate the moon base where there is water frozen in the rocks, and we then put a radioactive heat source in those rocks, will there really be no corrosion in the very long term? If we are wrong about that, could we end up contaminating the very thing we went there to use?
(We need some analytical risk thinking for ventures like this.)