Ok, so here are some other thoughts, some that are helpful here in the US. Not sure how easy it is for your situation with Scotland.
Are there any Military records that might exist? Draft cards have been immensely valuable over here.
Did Michael ever apply for a passport, and is that information accessible?
When did he move to Scotland? Would there be an immigration document? I suspect not given the marriage date, but I thought I would ask.
When he moved to Scotland, did he go alone or travel with others, which might help narrow down the townland?
Finally, back to my original note, if you have a lot of free time, and patience, you can walk through each Parish individually and look for matches on Michael Smith's birth in 1896 at the BRS site. It's tedious (and even more so now that they have broken the parish info into the respective religions), but I have had success with that in the recent past. That will at least give you some additional information.
You can likewise look for a potential marriage of Patrick and Bridget. This is trickier since you don't know when they married, and it is way more tedious than the Michael-birth exercise. Start with a date 5 years before Michael's birth (1891) and go with the +/- 4years. I would start with identifying the parish where Bridget Lynch may have married, and then for each match, see if there is a corresponding Patrick Smith. And if that parish lined up with Michael's birth, you could feel good, but don't get overly optimistic or pessimistic since the marriage likely occurred in her parish, but they may have settled in his.
And who knows, you might be able to then use IGI to find the parents of Patrick and Bridget!
Best of luck.
John