Well, as a questionable man of the law who is definitely not an axe murderer, I need a nice durable trenchcoat to deal with the sprays of blood from the axe murders I haven't been doing. Also, probably attacks and stuff since I'm going more martial minded than previously. He's a fighter.
He has his favorite axe, which is really for utility and not secret axe murders.
And a gun. Ideally I was looking for a longish-range shotgun, but all of those seem to be two-handed and up. Fair enough. So it's currently a Colt Python, though any sufficiently big gun will do. The idea is getting off a single shot pre-melee, so when they close in (or I close in) they're nice and softened up for some not axe murder, so big damage, bad reload is fine since I only expect to get off one shot, and one handed because I'll start with sword and gun held.
Beyond that, incidental items for a future sheriff. Manacles probably with key. Utilitarian rope and chain. Maybe a flask for the alcohol I'll need doing investigating all the axe murders. That kind of stuff.