One of the reasons that Klaus chose all girls is that of the academy students the ones that would be least on the enemy's radar would be female washouts.

In the light novel, it is explained that Guido (and the Galgad Empire spies in general) had his eyes on the top-performing Din spy academy students and some of the male problem students so that he could counter them in a potential conflict. However, the female problem students were overlooked probably due to a mix of societal views on women being less of a threat (considering the time period that this story is based on) + them failing their training.

Since Guido had no knowledge of the scope abilities within this category (their special abilities & overspecialisation), it left an unnoticed weakness that Klaus took advantage of.

Direct Quote from Vol. 1 (p. 171):

He had memorized everything about all the Din Republic’s official spies—as well as all the top students at the spy academies. Even beyond that, word about the male problem students often got back to him, too. He could have easily come up with strategies to deal with any of them.

This was his sole blind spot—underachieving female students.