Normally "nuclear capable" in the context of missiles means capable of carrying nuclear weapons, not having some sort of nuclear propulsion. Nothing in the FT article seems to suggest the latter.
There was some attempt in the 1960s to develop nuclear ramjets, but it was canceled. Allegedly because it would encourage an arms race.
Missles that are more than five times faster than the speed of sound and you’re worried about the environment?
Maybe you need to find out how they work, even just to test them without detonation. The propulsion variant.