Yes appears to be nothing recorded as to who made the decision to execute by firing squad. Tough call, when the man hadn't even got on plot to spy and send anything back to Germany!!
This whole story has always fascinated me because he spilled the beans very quickly as to his mission in full detail, but as the war was only in its infancy, I suppose he thought, he would surrender and he would be repatriated or some other life saving method where he would live for years!!
Not so my Nazi friend.