Uh... I don't know the exact procedure, but as a former tech, I would hate to not have COMPLETE access to the device am repairing.
You don't want to tech to give the phone a once-over to make sure everything is kosher before he hands u back the phone?
If you worry about private data, how about just changing your iCloud password.
General tech policy (again, am not familiar with Apple) is that if you hand me any device, I assume you already made a full back up because I am not going to guarantee you that nothing happens to your HD. A screen change should not affect anything but corporate liability's fine prints will have what I just said.