I wouldn't say the Germans "had" Simo Hayha. Finland's war against the Soviet Union was sort of a sideshow to World War II with little connection to the larger issues at hand. The Finns were fighting to retain their own independence from the Soviets, not to further the aims of the Axis powers.
The Soviets saw a chance to annex some territory while the rest of the world was otherwise occupied, as they did with the Baltic states, but the Finns did not cooperate. The Finns' alliance with Germany was rather tenuous and was very much a matter of "the enemy of my enemy is my friend." Under pressure from the Soviets, the allied countries did officially declare Finland an enemy nation but did not follow up with any kind of military force.
Finland was forced to give up some territory to the Soviet Union after the Winter War of 1939-1940 ("Just enough territory to bury our dead," a Russian general was quoted as saying) and, still stinging from this concession and looking to regain its lost territory, cooperated with Germany when Germany attacked the Soviet Union in 1941. When the alliance had run its course, and the Germans were clearly getting the short end, the Finns basically told the Germans "thanks for the help, we can take it from here, shut the door behind you on the way out." The Germans weren't too happy about this, and Germany and Finland actually engaged in open hostilities.
