The area around the station is safe. There is a line up of taxis outside to meet every train so I'd just hop in a taxi and go. As you say, it's not far but it's also not exactly a direct route as you'd walk thru the pedestrian area of the old city which is a little twisty.
I also suggest you print out a googlemap of the location of the Residenz am Zucherberg. I had that but the print was pretty faint and my cabbie did not know where this hotel was. It's really an Assisted Living facility but they have a hotel wing so it's not used that much by general tourists. I think it might have been 10 E or so for him to get me there but to me very worth it. He stopped to ask another driver as we were exiting the train station and they had a discussion about best route (my German is non-existent but that seemed to be the intent).
I was wondering about the hotel but wow, rooms are huge, breakfast was very good and I loved saying hello to the residents in the halls. You eat breakfast in a separate dining area.
This is a fun, fun tour! I hope you'll be there an extra night as there is a lot to see in Trier.