does this happen even when you are not sneaking around? is the entire melee system only "one button" style?
There is no real melee system. If you have one full energy cell, you get a takedown prompt when you get within range, regardless of whether or not you're sneaking. If you don't have a full energy cell, you don't get the prompt at all and can't perform any takedowns.
I actually used the stun gun against him to shut him down before shooting him in the back of the head with the shotgun. Then, when I hit him with the stun gun again and he died. Heehee.
Getting up close wasn't really a viable option for me. On Deus Ex difficulty, he can kill you in about 3-5 hits (with my health buffed to 190) and I didn't have the cloak aug. Barrel-throwing was pretty effective, though.