The exclusion zone is actually resembles a wildlife refuge these days. From reports of the numbers of animals present it seems like human populations are much worse for wildlife than low levels of ionizing radiation and other contaminants from the disaster.

The animals’ populations have rebounded, especially those, like wolves and foxes, who’s habitats are least compatible with humans. Still, mean lifetimes, fertility rates and mean body mass are down, while illness are up. This also applies to some plant species. In no way was Chernobyl a strictly good event for wildlife, just that removing humans took away a very strongly negative factor.

The radionuclides I described won't kill you quickly, but over a period of decades, and, well, it's more of a stochastic death as opposed to a definite one.

It may be that shorter lifespan wildlife just aren't as significantly affected, but I've no idea to be honest.