I agree with AJ.
Additionally, you should make sure any lockscreen mods or custom icons you can see from the lockscreen are hidden when you bring it in.
Personally, I would just put a password lock on your phone. They will be able to see if its charging it but wouldnt be able to see your home screen. After all, you're not there to get your iPhone serviced, you're there because your dock connector went bad. Don't worry too much.
You could also just have them test it on one of their devices. Say you don't have your phone on you (remember this isn't about your phone). If the dock is broken, its broken.