Hi!

No Etherdelta does not have access to your private key if you trade there. But they have gone through changes in ownership and the exchange is now owned by vague owners who I do not fully trust. There is not that much they can do if you use a Ledger except theoretically display a different send address than it's actually sending to. If you pay very good attention to the display of the ledger you should be able to discover if they ever do this. I don't think they do, but a while ago Etherdelta was hacked and a hacker replaced the site with his own version which did change the addresses, and people who paid too little attention got screwed.

I have personally moved to Radar relay and similar and try to touch Etherdelta as little as possible now.