In that county is Osojnik too. That is not Herzegovina, and I think that this confusion about his birthplace in Herzegovina comes from the fact that border is just across the hill AND Slano region, even today, is administrated by Franciscans from neighboring Bosnia-Herzegovina (they have their monastery in Slano).
I checked online Croatian phone book and found 28 Zarak telephone subscribers in Dubrovnik county, one of them is in Osojnik. That region is not large, maybe all these Zarak from the phone book have the same origin as your grandfather.
I’m not sure what this “Zuayne” could be. Maybe some small village near Slano. The closest “matches” I found in that county are ZULJANA and ZAVRELJE (there is one Zarak family in Zavrelje).
Based on all this, I think that we could say that your Zarak is from Slano area. If you are interested in making of a family tree, you should find records for Slano parish. Maybe you'd like to contact Tom Ninkovich? He does gen researches in Dubrovnik area every year: http://www.croatia-in-english.com/tom/index.htmlhttp://www.croatia-in-english.com/tom/index.html
If you’d like to find out if some of these Zaraks are related to you, you can write to them. I can translate your letter in Croatian.
Hope some of these new facts will be useful in your search.