No king of Denmark was a bodyguard for the Basileus, but there are two things you could be thinking of:
1) Haraldr Hardrada, who did serve as an officer within the Guard before heading home to claim the throne at home and invade England (only to be defeated by Godwinson in 1066), but he wasn't a Dane.
2) En route to the Holy Land on the (second?) Crusade, the king of Denmark (name slips me) visited with the emperor, who treated him far better than the other crusader kings, because he was the king of his bodyguards.