No, not swapping the whole strap round, just attaching the clasps the other way is all, so the swing part is on the case and the catch is on the strap, the rest of the case as is. That way you have gravity working for you rather than against It would also mean that there's less metalwork on the strap when you open it.
I do love the design though and I've just got some of those button studs with the rings in to experiment - I missed them the first time round, they look great!