Is it possible to disable Siri on the lockscreen while not requiring a code to unlock the device?
I'm using iOS 7 and I think this was possible in iOS 6.
Yes, under Settings -> General -> Passcode Lock you have a section named "Allow access while locked" and there you can set Siri, Passbook and Reply with message to off.
Edit: Oh, sorry, didn't see that you mentioned without having an unlock code. I just tested and that didn't seem to work, even with activating the passcode lock, setting Siri to off and then deactivating the passcode lock. The switch is in the off setting but Siri still activates.