As it turned out, the type of swaps that would be happening would be body swaps.... ish.
Whenever two people swapped, they would exchange their height, body shape and hair style.
As such, they would end up looking mostly like their counterpart, albeit with their original face, skin tone and hair colour... and their genitals. Except for the shape of their face and their junk, it would be almost as if the two had swapped their shadows and everything that made them that shape.