Both quick finds and Perform find can be scripted.
But if the layouts are identical, why do you need two layouts?
Just enter find mode, specify the country as your search criteria, perform the find and stay on the same layout. What you see on the screen, if the two layouts are identical, is exactly the same, but now you have one less layout to maintain.
And the steps that I just indicated can be automated. As an example, you can add a global field to your layout and format it with a drop down list of countries. A script trigger on the field can perform a script that uses the data selected in this field as find criteria. This script can also switch to different layouts for different countries, but if the layout is identical, there is no need.
For examples of this scripted find and others finds, see: Scripted Find Examples