That's interesting, and it sounds very likely that that is how he would have written it. Here is a page I found with stuff about Casey, and about the Inny, with some photos

The question is whether he'd have changed it himself, and if so for those reasons, or whether it just changed in the process of being overheard and sung, because it slips off the tongue more easily as "shining" than as "Inny". I never got the impression the Fenian songwriters were averse to including place names in their songs.