Would Cherenkov radiation occur at the explosion of a nuclear bomb? Suppose it would not be occluded by smoke or anything else for that matter.
Of course, you could observe it in the water where the speed of light is much smaller than $c$ and electrons (beta-radiation) from the nuclear blast easily beat the light.
The air has index of refraction $1.0003$ so the speed of light is $0.9997c$. Note that $v^2/c^2$ is about $0.9994$ and when subtracted from 1, we get $0.0006$. The square root of it is about $0.025$ so charged particles get about 40 times heavier at this speed.
Clearly, this is about 40 GeV for protons or neutrons (and even more for nuclei), so you can't get this fast hadrons or nuclei in a nuclear blast. Even for electrons, 40 times the rest mass gives about 20 MeV which is, I believe, much more than the energy that an electron can ever get in any process of this kind. Moreover, fission really produces two smaller nuclei that carry the energy away, and the energy of a neutron that is created is just 2 MeV or so.
So you can't get Cherenkov radiation in the air by nuclear blast. Cherenkov radiation in the air is a strange animal, anyway: we usually talk about water or similar dense environments. How air usually enters these discussions is only via the supersonic analogy of the Cherenkov radiation - but when dealing with sound, it's not the real Cherenkov radiation. ;-)