I see your argument but is this (biting around) really happening or it's your worry? My experience (one data point!) with dogs I've seen is that they're totally concerned with their quarrel, not bothered at all with passersby...
There's nothing good that can come out of this. The likely outcome is a dead small dog and a vet/physician bill. I'm not risking a hand injury over someone else's animal, hand injuries can be disabling.