The dominant hand is the one which is most dexterous. With a guitar, it is actually the picking hand because this needs the delicacy and accuracy more, especially when learning. Obviously, with an accordion or melodeon, it needs to be the melody hand.

I play the English concertina, because it's totally ambidextrous. I play piano accordion occasionally, upside down. With a melodeon, you can't reach the air valve with the instrument upside down. Although it could be modified, that's a bit like turbocharging a Lada in my opinion.