Fortunately, a nuclear reactor isn't radioactive until the reactor is turned on. Enriched uranium on its own is hardly radioactive at all (U235 t1/2=~700Myears); depleted uranium has meaningful safe non-nuclear applications[0]. There are orders of magnitude more radioactivity in the RTGs already used on deep space missions. Those are very carefully protected, but the risks are deemed acceptable. So long as you don't turn your reactor on until you're well away from earth, I see very limited risk of exposure to the public, far less than from a RTG.

[0]https://en.wikipedia.org/wiki/Depleted_uranium#Civilian_appl...