One reads in old novels that a character “shot his cuffs”. I’m fairly certain that it doesn’t mean he violently snapped his arms straight out and caused detachable cuffs to fly like projectiles into opposite corners of the room. But beyond that I’m vague. I can’t guess.
When you’re wearing a long sleeved shirt and/or a suit coat, the sleeves (the cuffs of the shirt) come down to cover your wrists and the tops of your hands sometimes. If someone needed to check their wristwatch or do something that could get their hands dirty and wanted to not get their shirt sleeves dirty, they would snap their arms out, which would pull their cuffs up on their arms, baring their wrists.
You’re about halfway there, actually. To “shoot his cuffs” means he exposed his cuffs by extending his arms, thus making his cuffs appear from under his jacket.
I encountered this just a few days ago in Snow Crash by Neal Stephenson. I got from the context what he was doing because I can picture someone (he was a mafia guy, iirc) standing quietly and waiting for someone to do something for him.
I picture, strangely enough, Beetlejuice, in the marriage scene (with his lovely purple tux) popping his cuffs out from under his jacket. He pulls one, then the other and then pushes both arms forward quickly. That’s a terrible description, but if you watch the movie, you’ll get what I’m saying, I hope.
The “shoot your cuffs” expression turns up in or about 1900. The forerunner to that, which goes back another 20-30 years was “shoot your linen.” Meaning the same thing.