The best I can think of is to add an entry into the db directly for the Country list. It has to be added to the db directly as adding to the predefined values list will not save a blank value. You can use the following query (or modified as desired):
INSERT INTO `sys_pre_values` (`Key`, `Value`, `Order`, `LKey`, `LKey2`, `LKey3`, `Extra`, `Extra2`, `Extra3`) VALUES ('Country', ' ', '0', '--Any--', '', '', '', '', '');
Clear cache afterwards.
This will enter a blank value for the country - although your users see --Any--
Note: using the --Any-- (or equivalent) will also make using this field in the search parameters easier.