If you apply a distortion effect like Crystal ball, you will need to account for it when determining which tile was clicked. There's probably a formula, but I don't know it.
Also, I don't think it's possible to change image offset in runtime, this property is only available in editor. I guess it's not really needed, you can use two copies of the tilemap, or put two maps on one tilemap, and move the entire tilemap. But, you'll still need to prepare the array of all tiles and their corresponding countries. With 198 countries I imagine the tiles need to be quite small and this array will be really big...
As for my first suggestion - distinguishing 198 countries by color may not be very accurate. You need to put a small Drawing Canvas object in the position where the map was clicked, paste the map onto it, then do "Drawing canvas save snapshot", and after that you'll be able to read RGB values of the pixel.