Necromancers and Sorceresses (except for Light ones) can accidentally kill the King of the Minotaurs with their spells, which results in a permanent closure of the cow level, so Fury and Trapper are the best choices in this regard, and a Light Sorceress can also work.
Among different characters, only the speed of clearing the cow level as a whole matters, which is especially high for Trapper and Fury. It's all quite simple.