No, he isn't a coward. If he were one, he certainly wouldn't be an Investigator at all.
Rather, the indication in Ch. 53 was that he kind of....knew what was coming and wanted to avoid it as long as possible. He was obviously very close to Hairu, and her loss in particular hit him incredibly hard. So he wanted to avoid seeing her dead for as long as possible.
We see that even in his shock, he was still getting the job done. We just got to see into his mind, and what was going on there while on the outside, he probably looked fine as always.