It was Kevin Conroy, and Timm has confirmed in an interview that they had him record the line anew -- although as part of a recording session for something else he was doing for them, so they didn't bring him in just to say two words.
I'd like to know who did the other voices, though, particularly Strange. He sounded a little like Jeff Bennett, but I'm not sure. Come to think of it, it could've been Corey Burton, who played Strange in Arkham City (according to IMDb).
And the big guy was based on the creatures in "Doctor Hugo Strange and the Mutant Monsters" from Batman #1 in 1940. The shot of Batman firing a machine gun from the Batplane was also an homage to that same story, since that was the infamous issue where Batman strafed a truck and killed the drivers, then hanged one of the monsters from a rope dangling from the Batplane.