I'm not familiar with 737 procedures etc, but I would definitely shut the engine down if the other wasn't showing any signs of problems. It's so easy to screw up the approach if you have one engine running at 77 % if you have never done that!!!
In my opinion, your instructor just loves this scenario and knows an easy way to handle such an approach, but what if you have never done it before???
If you feel more comfortable shutting it down, for christs sake, shut it down.
GDAL