Drill groups won't work that way, and a cycle will require 2 clicks.
To do this 'on click' you could include 2 dimensions (Region and Country) and conditionally show one or the other depending if 1 or more Regions have been selected
No Regions Selected
One or more regions selected
The settings are on the dimension tab on each dimension itself, here is the condition for 'Region'
Region 'enable conditional' expression: GetSelectedCount(REGION)=0
Country 'enable conditional' expression: GetSelectedCount(REGION)>0
Test.qvw 227.5 K