Everyone is talking about dominant and recessive genes, so I just want to clarify a couple things.
The way your body directly uses genes is as a blueprint to construct proteins. Your cells are always producing proteins from the genes in all your chromosomes. It has complex ways of regulating how much of each it produces, but your body doesn’t care what chromosome it’s coming from. Once an embryo is fertilized, there’s really no distinction between “mom” chromosomes or “dad” chromosomes, as far as the embryo and its protein machinery are concerned.
“Dominant” and “recessive” characterization is about how those proteins affect your body at the macro scale, not whether your body actually uses the gene and produces its proteins – it always does that. For example, brown hair is a dominant trait, and blonde is recessive. But this is because producing any amount of brown pigment will make your hair brown, regardless of what other pigments you’re making, simply because it’s darker. Literally the same as combining blonde and brown paint. It has nothing to do with whether the genes are actually being expressed – the brown hair gene doesn’t stop the blonde hair gene from making its pigments.
I almost hesitate to bring up the other problems with your plan since, obviously the total monstrosity of it. But that’s anyway pretty well covered so I’ll just throw in that blowing enough nukes to kill that many people would create considerably worse environmental disaster