Does the paper have a thin plastic layer to make it waterproof? That stuff is sneaky and turns what looks green into a recycling nightmare. Your customers might not realize it can't go in the blue bin. Reducing waste is awesome, but only if the whole product breaks down easy. I've seen places switch and then their wrap just messes up the whole recycling stream. It's worth digging into the specs before you celebrate the win.
That "sneaky plastic layer" is everywhere once you start looking for it. It's in so many things that seem eco-friendly, like those paper coffee cups. At this point we need a detective just to figure out our own trash.
But honestly, how many people are even recycling that stuff right now? Like @amy_anderson said, it's everywhere, so most of it probably just gets tossed anyway. The switch to paper is still a step in a better direction, plastic layer or not.