Yes, this usage of Vて＋しまう conveys the regret and/or lack of intention surrounding the circumstance - specifically, that the pitcher threw the ball in a way that it hit the batter, rather than in a way that allowed the batter to strike the ball. So, I think your understanding is correct.
However, how you translate it is a question of your purpose (e.g. to entertain, to inform, to persuade), and your audience (e.g. assumptions about their skills and knowledge, how formal you need to be with them, etc.), and personally "hit by pitch" only adds to my confusion as someone who is only familiar with baseball in passing. I'd therefore consider a different translation for a novice audience like me (noting that how you make it sound natural in English will depend also on what else the text talks about), perhaps something like:
"Moreover, in Japanese professional baseball, when a pitcher's throw
unintentionally hits the batter, he/she takes off his/her hat and
apologises. Could we not say that this too is another form of [the] heartfelt
courtesy [shown in various settings within Japanese society]?"
with bits in brackets are inferred from what I'm guessing the rest of the text talks about.