You must use any IC/ICE listed on your ticket (the actual ticket part should refer to them, the itinerary will give detaIls).
If your journey includes sections with regional (RE or S) trains, you are free to use later or earlier services, and to use any route within the limits shown by the station codes (these are often very generous). In your case, I imagine you would be free to travel via Köln, but you would then have to take an RE to Duisburg not an IC/E.
In practice, though, if you show your ticket to the train crew at Köln before you board, they are very likely to allow you to join your booked ICE direct to Hamburg. But to travel an hour later you would need to show that you had been delayed - just as with an Advance here.
Just seen Quakkerillo's reply, which I suspect lists exactly the trains on your original itinerary. I would only stay on board the ICE to Köln, which he suggests as an option, if advised/endorsed by the crew - but in that case you should have no problems using the EC (Swiss stock with restaurant car BTW), and you'd avoid the class 425! Depends if you want to be an hour late into Hamburg.