I just use a large mesh strainer like you'd use for spaghetti. The bowl I use looks something like this:
Even when the grinds look even and bigger than the holes in that mesh, which they should, a few dozen seconds of light sifting will get rid of a decent amount of fine grinds that way.
As for the Mizudashi pot I use, I broke one and have three working ones, that means an extra non paper filter and easy system. I don’t have experience with the cold brew bottle, but I’m pretty sure you could make that work. I like the pitcher, in part, because of how easy it makes measuring the beans both pre and post sifting.