fluffy might not work, and "fluffy" usually is not from the vermin's point of view
ie a displaced rat is probably a dead rat quite soon, from a nest and into a pig pen is horrible to listen to but etc
if i understand properly, preserving the site is important
put watership down behind us
get em gone as kindly as possible, dead may be kinder than displaced, both is probably as good as is might be
Apart from their setts, badgers also dig outliers, which are inhabited during the spring and summer. We think these might be for displaced badgers when there are cubs in the main sett, as we have seen no evidence for them being used at other times of the year. They are also good at making scrapes looking for food and digging shallow hollows for latrines. The trick with the latter is to find them before they find you.