My pan has a lip either side - you can pour and stir at the same time using whichever hand you choose. It didn't come from a specialist shop.
AS for Janie's apple peeler, I have never used one (except a knife), so I have no idea which way round they normally go.
I usually use my left hand for things that require strength, like opening jars, so it is not the "weaker" hand.
Old sewing machines have the handle on the left and the needle on the right, but so did the even older treadle sewing machines, powered by foot action.