To bring this all into context, here's what it looks like now:
If you can make a up an elaborate story which explains why cleavers were always carried that way, I will consider it.
Once upon a time there was a butcher. He had a shop on a street in a large town. One day, the meat delivery arrives. After the unpacking he sets to chop up the large carcass's that had just arrived. In front of him is a particular large chunk of meat, he couldn't simply use one of his knives, he had to use his cleaver. As he reached for his cleaver, due to the way it was sheathed on his body and the fact he is right handed, he accidentally, used the blade to pull out the cleaver as the handle was to awkward to reach for. In doing so, he sliced 3 fingers of his hand. Blood spurted everywhere, and the local doctor was called to save him...
1 month later.
The butcher was overseeing his son doing the butchering (he couldn't do it any more due to the lack of fingers) and noticed that his cleaver was in a strange place, not the usual place. It was sheathed like a dagger would be, not hampering any movement, with the handle easily reachable. He saw his son reach for it and in one fluid movement he pulled it out and started chopping.
He asked his son "what made you think of putting the cleaver there?"
The son replied "it just seemed natural, was I wrong, am I not doing it right?"
The butcher said "no, no, carry on, your doing great".
That night.
The butcher couldn't sleep, he couldn't stop thinking about the genius of his son's idea. He couldn't stop thinking if he had the cleaver like that 1 month ago, he would still have his fingers..
THE END.