I think what would be better is an option, post-snap-taking, to remove things from the image. I don't mind animals, myself, but have often found myself getting quoins so that they wouldn't be in the image.
When I first saw sticks, when a player was accidentally given one by Rube before they were released, I thought they were going to be used on public streets, not as a replacement for pens. I thought they would be a thing where you could attract the animals to one space to nibble/squeeze/milk.
Of course, with pens gone, the current use is useful, and what TS have thought of, but I believe this idea has its merits too.
Perhaps a time limit of 5 minutes before the stick is unlocked and no longer magic.
I love this idea. :: nods :: Especially with a time limit, then your stick would be automatically returned to you.
Or if you could, as Lemo suggested, have a switch to turn off certain things in the snap so you don't capture them, like speech bubbles.