Off at a tangent:
The reason for the B/C box arrangement is that the key of C has all the naturals, and the key of B has 5 sharps, therefore providing plenty of accidentals for playing in all the other keys i.e. G, D, A and E as well as B.

I can't off hand think of any Irish tunes played in B. There was one I knew in E but can't remember what it was- and there are several tunes commonly played in A: the High Reel and the Mason's Apron, from memory.