Shaw makes Captain Bluntschli Swiss because he wants to make clear that Bluntschli is not fighting the war for patriotic reasons at all. He is simply a mercenary, fighting because it earns him a paycheck. He doesn't care who wins, and he is very clear that the war is neither heroic nor glorious to him. In fact, he thinks is it ridiculous. He carries chocolate bullets, and he deserts, which is why he has to hide out from his pursuers in Raina's bedroom. As he explains to Raina, in his view one side only ever wins a battle because they are less incompetent than the other side. All of this makes him a complete foil or opposite to the romantic Sergius.
Bluntschli is also Swiss, rather than Serbian, because his nationality emphasizes his outsider status. Switzerland was traditionally a neutral country, one that didn't get involved on one side or the other in wars. Bluntschli, likewise, has no interest at all in the relative merits of the Bulgarian versus the Serbian cause. He can stand outside and above nationalistic passions because they don't matter to him. This makes him a hard-headed and reliable judge of what is going on. He is able to function as Shaw's mouthpiece in puncturing romantic illusions about warfare.