It probably would have been clearer if the OP had specified either UN members, or countries that are widely recognized as sovereign, either of which would exclude Wales. By either of these criteria, there are only four countries that have one-syllable names in English (France, Spain, Greece, Chad); or five if the one-syllable pronunciation of Laos is accepted.
I don’t think that most people would consider Wales to be any more of a country than Catalonia or Hawaii are.