That is a chicken and egg problem. Look at argentina pre Miley, when the dollar/peso exchange rate was fixed and you couldn't freely exchange. People would still prefer the dollar over the peso, even though you couldn't legally agree on dollar prices in contracts such as rentals. So people were using the dollar to save in, and exchange for peso when they needed to exchange goods.

My point being, you can have two competing currencies and exchange between them. In Argentinas case, the currency competition was healthy as politicians couldn't conceal their bad financial policies due to the hyper inflated exchange rate for pesos.