I often trade my ERC20 tokens on Etherdelta but I never enter the private key for my Ethereum address because I do not trust their website which can be hacked. I always use the Metamask plugin installed in my web browser.

Some naive customers enter their private keys on the Etherdelta site, so the administrators of this decentralized crypto-currency exchange may be collecting these keys. Thus, theoretically, you can try to ask your private key from them, but I am pretty sure they will reject your request because Etherdelta has a good reputation.