Cash exchanges would have a much higher transaction cost in terms of spread.
Even if you found a exchange company who will fill your order of the exotic, they have higher overhead since they have to take delivery of notes and pay a clerk and rent to run a storefront. In most cases, the average spread is ~1.5-3% padded onto the interbank quote at these places for liquid currencies (Euro, AUD, etc..) let alone exotics which can be more.
If you find a broker that trades in your desired exotic, you'll likely only pay a fraction of the cost to do the exchange, but you might have to pay a cost of carry on the position (even if it's low leverage).... this, of course, could work for you if there's a positive interest differential on your position (which you wouldn't see holding the physical cash.)
So there's a bit of a trade off. The right choice comes down to exactly what currency pair you want to trade, the leverage amount, how much you expect it to move (making the wide spread not matter as much) and how important it is that you can buy/sell it at a moments notice.