Well, some people suggested that it might be good to implement simple wallets for the coins and connect directly to the coin's networks, but it seems to me to be needlessly complicated. So far I prefer to connect to other clients, that provide wallet functionality, via their API. Currently, I already have some support for bitcoind-like API and would like to add support for Electrum and possibly other clients as well.

It should be pretty safe way of trading, although probably not the cheapest and definitely not the fastest (because it's happening on blockchains so one has to wait for confirmations).