Considering he fought off a troop of Union Soldiers until he was killed, I would say he was no coward.
Booth fought off nothing, according to accounts of those there. He was shot early on and spent the next few hours dying a slow and agonizing death.
He didn't fight anyone off. He was trapped like a rat and even his demented mind realized after reading the papers that even the very real Confederates of the day (not the BS Internet neo-confederates of today) considered him to be a cold blooded murderer, not the hero his demented 'actor' brain thought he was going to be. I could see one of these Hollywood super-ego types doing something like that today. Their egos are just as grand as Booth's.
Booth was every bit as crazy as Oswald, Guiteau, Czolgosz, Cermak, Fromme, Moore, Hinckley, and Arutyunian. All little men (and two women) who were obsessed lunatics.