How can I share smoothing across objects?

If I have two objects that share edges (eg, if I separated a few contiguous faces from a sphere into their own object), is it possible to have the objects smooth together as if they were one? Ideally, this would hide the seam between the two different objects.

Both objects would be skinned to the same rig - we’re basically talking about, maybe, a nose separated from the face and smoothing the joining edges.

Why not just re-join them? If they have contiguous edges, there’s no need for duplicate geometry, and with that duplicate geometry, you aren’t going to get smooth shading unless you use custom normals

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My current thought is that I’d like to have data unique to the object - shapekeys (so I can keep them organised and not affect the rest of the mesh) and uv islands (so I can use UVWarp without changing the layout of the rest of the model).

Custom normals, eh? Might look into that - if you have any other suggestions, I’d love to hear 'em! =D

The simple (probably) way to acquire Custom Normals: make a copy of both meshes, join them, merge the edge.
Now use Data Transfer Modifier on the separate parts and transfer Face Corner Data > Custom Normals from that combined object. Apply. Also probably check Object Data Properties > Normals > AutoSmooth to be able to see custom normals.