Going over his findings is one of Donnie's thoughts- better done in a place he won't be immediately compromised. He tucks in by the foot of one of the displays once he's back in the trophy room, slipping out the patrol map for a better study of its contents.

Maybe if he went out through one of the office windows he could just circumvent security completely, but he has no idea what that side of things looks like or how smooth the walls would be. The halls don't offer much by way of cover so if anything, he's better off taking the less-direct ways again and figuring out the loopholes in the security postings.