I think what happened was..
Booth walked up to Lincoln, reached around and stuck His eye with a dagger, yanked His head around, pulled out the dagger and shot him in the same eye. Dropped the dilenger. Jumped the balcony, said his words, while waving the pointing the dagger in the air and left. "dagger" would of been more dramatic for an actor vs a little handgun.
He didn't need the gun after he shot him. It was left on the floor in the booth. Those in charge had that. So why then was Ford theater torn apart? What were they looking for? They were looking for something they knew he already had. At that moment all he had was his diary and the dagger. It can only be these items at that moment he carried they wanted. WHY is a million dollar question. The diary could only lead to a conviction, which wasn't needed obviously, since everyone knew what he just did. So that leaves only the dagger. The dagger, the dagger...so little gets said about the dagger. They didn't catch Booth until he didn't have it in his possession. WHY?
History recorded then, that he gave a gift to Mrs. Quesenberry and today history says "maybe it was his boat".
The "WHY" is special.