Your interest in working at a "Nuclear site that doesn't have operational cooling stacks or the such" makes me think you can't be trusted and should look for work in another industry......unless of course you have an alergy to "cooling stacks or the such".
oh that's silly,...
there are convicted felons in DOD, DOE, etc.,...
the vetting is stringent and the access is never guaranteed just because you apply but it is possible,...
probability is a different discussion,...
and lots of nuclear facilities do not have operational cooling stacks or the such,...
and the folks who work there are,.......wait for it,.......nukeworkers,.....