People usually referred to their birthplace or place of residence by using the name of the relevant "townland", and in rural areas there was usually no other form of address to use (no street names or numbers, in other words). Wikipedia has a good article discussing what townlands are, in case you're not familiar with the term. If he said at his marriage that he was from Scrahan, then it's very likely he was referring to a townland. Emigrants did sometimes refer to where they came from by naming the nearest town of any decent size, but Scrahan is very unlikely as a town name. The Irish form of the name is An Screathan, which means "the scree hill/slope".
There are two townlands called Scrahan in County Cork, and one of them is located in that very parish I mentioned, Iveleary/Inchigeelagh. You can see more info about it at this link:
https://www.townlands.ie/cork/west-muskerry/inchigeelagh/bealock/scraha…
The parish registers for Iveleary which are available online (for 1816-1880) can be accessed at this link:
https://registers.nli.ie/parishes/0062
The other townland with the same name is located a couple of parishes to the north, right on the border with Kerry, and you can see more info about that one at this link:
https://www.townlands.ie/cork/duhallow/nohavaldaly/knocknagree/scrahan/
Comparing the maps, I think that townland is in the parish of Rathmore, which lies mostly in Kerry but partly in Cork (with Scrahan being in the part located in Cork). The parish registers for Rathmore which are available online (for 1837-1874, with a several year gap in the 1840's) can be accessed at this link:
https://registers.nli.ie/parishes/0091
Searching a parish register can be time-consuming (though also very interesting), but you can download the pages of likely relevance and search at your leisure, enlarging them as necessary to deal with handwriting which may be hard to read. The entries are usually arranged in a pattern, so once you figure that out you can often just skim down the relevant column. You have some target years to start with, but keep in mind that people in rural Ireland back then often had no idea exactly when they were born, since there were no civil records to consult and they usually had no personal written record of it (no family bible or anything like that). There were census records, but most of those were later destroyed by fire in the 1920's. Even in those that exist, the ages of people are usually estimates, and often disagree from one census to the next (same problem with censuses and other records in the countries to which people emigrated - one has to be cautious in accepting the ages given, as they were often guesses).
Both of those Scrahan's are in O'Leary territory, but I'd try Iveleary first, since there are more O'Leary's there. You might also do dna testing and see what matches you turn up. Good Hunting!