I had checked out the COTEOF possibility a while back and felt it was not a good match. Here's a closer shot. Note the clouds. They don't seem to be present in any way on the piece in question. It's also lacking the striated color that the mystery piece has. If the mystery piece IS this planet, it should be a simple task to match it.
There's only a handful of planets used in TOS. They then recolored or flopped as needed, or simply reused as-is. An Earth globe was used fro a lot of instances, usually flipped around and upside down to throw things off.
Most show definite cloud swirls. Very different from the Globe of Mystery. Unfortunately.
I'm still thinking "Apple fruit". After all, it's styrofoam so it would be easy to hang due to its light weight.