The placename Corcaigh has the genitive form Chorcaí. As usually happens with articleless proper names, it is lenited in the genitive. Moreover, though, the genitive has –í instead of -igh, and if you know anything about Munster dialects, you know precisely that this has relevance for the pronunciation – word-final igh‘s and idh‘s are down there pronounced as ig‘s, which of course does not happen with the long i.
The big question is now: why does it end -igh? You might have checked Ó Dónaill’s dictionary and found the noun corcach, which means “marshland” and has the genitive form corcaí. This is obviously the word we have in the Irish name of Cork, but what is the -igh form exactly?
The answer is: it is the dative case. Feminine nouns ending in -ach end in -igh in the dative singular. Your standard grammar will tell you that the dative case is not part of modern Irish, but the fact is that it is still used in many traditional expressions.
I seem not to be able to find Máirtín Ó Cadhain’s book Ó Cadhain i bhFeasta, which is among the first ever books I have read in Irish, but I remember from it that Ó Cadhain in one article criticized the way how official lists gave place-names in nominative case, while dative forms would have been more traditional and correct, in his opinion. Well, at least Corcaigh is given in the dative form!