Okay, at the risk of being unmasked as a total idiot, wouldn't you just refer to the brass on that diagram as "the tube?" I do think of the bore as more of a flute, clarinet or oboe term which references the cut on the inside of the body, and, therefore, in the case of the flute, the corresponding outside appearance. Or the bore itself being "the interior chamber" if I use Wikipedia as my guide.
So, while a whistle does technically have a bore, the term seems a bit highfalutin on the humble whistle.
So I would refer to my flute body as a body, not a bore. Most simple system wooden flutes we use for ITM would have a conical body corresponding with a conical bore cut.
All this being said, I often do refer people who live far from Irish whistle teachers and communities of musicians to the teaching on OAIM. It seems particularly useful and systematic in the whistle and concertina courses, and can provide folks with a virtual session to play along with at various speeds. This sense of community seems to have grown with Covid adding monthly zoom play along performances att a leisurely pace, perfect for beginners.
I subscribed to them a number of years ago when I was starting to explore the concertina. I did find myself wandering over to each of the tutors in all the instruments and learning something from everyone's take on what they were playing. There are some very serious players putting some great stuff out on that site.