Well admittedly I haven't yet worked out how to do it with the larger species, but a remains completely out of sight in a Harkila roe sack that to the untrained eye just looks like a rucksack. And a roe deer folds down into my large collapsible ice box. Inside the folded flat icebox is a similarly foldable luggage trolley. So that just looks like I'm going to a large picnic. Which isn't hugely off the mark. The key thing is that all of these things are watertight and there isn't blood dripping off the train's overhead luggage racks or anything like that.
Similar approach to wildfowling only it's mud that's the problem, not blood.