Fiat banks are for sure scary.
Probably it would be best to go with a secure fiat storage of your own, not deposited in any bank accounts but, rather, as physical currency in a safe or safe-deposit-box, and only trade "tokens" representing that securely stored fiat on the exchange.
That way all the risk involving fiat banks can be delegated away from the actual exchange-per-se onto third party (or nominally third party; you could run one of thse yourself in addition to running an exchange if you wished) "
market makers" who sell people the tokens in return for fiat and buy the tokens back from people in return for fiat.
At first glance this might seem silly, as the first question to pop into your head might be "what for do I need the exchange if these third parties exist, surely the third party could sell me actual fiat instead of tokens representing securely stored fiat???"
However, the big important difference between actual fiat you give to or get from these third parties and the tokens representing securely stored fiat (which you also get from these same third parties) is the "securely stored" part. Bank accounts are not secure in this sense, because what you think is in them can later turn out not to be in them due to transaction reversal by the bank. The "securely stored" fiat the tokens represent, by contrast, cannot be reversed thus are eminently suitable for exchanging with other irreversible currencies.
Another difference is all the fees these third parties would tend to need to charge due to the risks they take on in dealing with banks.
The actual exchange per se being separated from that risk and thus its associated costs can be nice and economical, letting you trade currencies without having to charge a percentage on each trade. (For example it could be implemented using-or-like Open Transactions, charging flat fee per action performed regardless of how much value that action exchanges or transfers.)
Thus once you have gotten away from the fiat banks into the secure tokens you can trade back and forth between umpteen currencies over and over and over again wheeler-dealing daytrading or whatever at far far lower cost (at least as long as your trades are not as tiny as the tiny nominal per action fees per action) than you could on exchanges that incorporate the bailing in and bailing out (to/from fiat banking sytem) risk costs into the actual trading system where the wheeling and dealing is done.
-MarkM-