Right, wooden arm...
I assume you're talking about a perm. shack, not portable? If that's the case, attaching to the wall should be doable with just a metal "L" bracket...
If you wanted it removeable, or able to swivel out of the way, you could mount a block of wood to the wall, arm from rattle reel on top, with a drilled hole & a pin down through the whole shebang...
Just tossing ideas out there....
FWIW, there's wall mount rattle reels available online, but they might all be too short.