How about just using a Combo Box?
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By a user being required to just choose what country they are from, it removes the unnecessary step of a user needing to first select the region (or you can just infer the region based on the country selected if needed). Allowing a user to start typing the country they are from will also narrow down the options available to choose from (an advantage over listing all options available in a dropdown list / graphically).
Smashing Magazine wrote an article about redesigning the way countries can be selected (they landed on using a combo box too). They documented their design process for this quite nicely too and is worth reading. There's also a live demo and a GitHub repository.