Would you still want them to be able to change the Country dropdown? Why show a list if it is already selected with the correct value?
Why not just show the country associated to that region in plain text in a div next to it? I don't think you need dynamic dropdowns in this case, since you are only going to have one option available for each selection.
I think you can probably add the country name to the original region list into another attribute like:
<option value="<?php echo($rs->getColumnVal['RegionID']); ?>" rel="<?php echo($rs->getColumnVal['Country']); ?>">"<?php echo($rs->getColumnVal['RegionName']); ?>"</option>
If you want them to be able to change the country and just have it pre-selected, then use the CountryID column in the rel attribute, if you only want it displayed and not changed, then I'd do an inner join in your Region recordset and put the country name in the rel attribute so you can populate the innerhtml of a span tag next to it.