I'm incorrigibly curious, and discovering the contents of the locked containers (of various types) in the Arcaneum in the College of Winterhold is something I've always wanted to do. I was wondering if Urag awards you with the key once you've completed his fetch quests, or if you have to pickpocket the key off him (I haven't been able to activate the "Pickpocket" prompt).
Further, none of the quests he gives you results in you getting the key from him. I don't believe it is possible to get it by killing him, since he's flagged as essential. I think you're just going to have to "look and not touch" in this case.