You can just run NM directly into the back of the handy box using a regular box connector (4040) or a locknut connector. If there is any chance of physical abrasion of the NM then just use a short run of PVC conduit through the wall. You can always glue a male threaded adapter to the PVC and where it enters the box use a lock ring to secure the PVC.

Thanks, bigbird. If the conduit is just to protect against physical abrasion, then THHN in flex (or MC cable) would be ok too, don't you think? All else being equal, I'd use a PVC sleeve like you suggest, but I think the flex will go through a smaller hole than any PVC conduit will go through. That stone is tough stuff.

There won't be any significant abrasion, regardless. I'm probably over-thinking this.

I'd ha' pushed a short length of UF through the wall, but can see nothing wrong with these other applications.