The end result could be anything up to and including war. The best solution in the service of justice would be for the third country to suspend Diplomatic immunity and arrest the Western world leader and then turn him/her over to the World Court in the Hague.
However, I think you have misunderstood the actual question.
What if the "third" country are closely allied countries such as France, Belgium, Holland, Luxembourg, Spain, and Italy, etc, as opposed to the North European nations such as Great Britain, Germany, Denmark, and Sweden, etc?
For it is near inconceivable that Italy would not grant diplomatic immunity to an assassin assigned by the French secret service because they allegedly favoured a Third world dictator over their own people; and it's near inconceivable that the Italian government wouldn't cooperate with the French authorities to cover up such a conspiracy between the two Allies in favour of people who are genetically Non-European, because such a violation of scientific law would beggar belief for any sane and reasonable person of education.
Actually, I honestly believe that there will be a war between the two countries, but not for the reasons you have suggested.
For the outbreak of war would not be due to the perpetrators being uncovered (due to a massive cover up by the so called "third" country, which would be Italy in this particular example), but the perpetrators would actually start a "war" against the Non-western country by using unconventional methods to overthrow a numerically superior ENEMY.
Ultimately, such a turn of events would be nothing short of outright humiliation for the deposed dictator to have been deposed by the Special Forces of a Western nation, and outright humiliation for the regime as a whole.
Such a spectacle would be outright humiliation in front of the world's media, and utter humiliation for the country as a whole, with no chance of reprisals whatsoever.
Since the Western leader would be doing Russia, America and NATO/EU a favour by shooting such an outsider who is not part of Western civilisation at all.
Consequently, there will be no reprisals at all, none whatsoever.
