When I miss a day, I don't stress it. The next day I simply make sure to make it a priority so I don't get out of the habit of doing it. In the past when I felt so guilty about not completing tasks I would find myself frozen and all of a sudden those habits I had developed were lost. Now I don't focus on it. I just move on to the next day with the intention of completing the task at hand. I have found this to be helpful.
I'm not sure if I'm understanding the question, but I think the point is not to break the streak. I fail at the challenges sometimes, and I just have to use that as a motivator to do better. Skipping and having to start the streak over is part of the learning process.
It’s ultimately your decision, but in my opinion, I would do both. In the morning, write what happened the day before and then at night, continue your normal routine.