The short answer is that it is not one of the original props. And given that, I figured you deserved an analysis of what was in the picture.
The thing is, this seems a lot like the situation of the TOS Enterprise model on display at Paul Allen's Sci Fi museum. The owner of the model believed that it was a studio model (used in DS9's "Trials and Tribble-ations") and had a receipt from Viacom. It wasn't the studio model, but one of a half dozen custom built models using the molds that Jein had used to make the studio model.
Adding that story to what we are seeing with these props makes me wonder if these people at Viacom were playing a little fast and loose with the facts to sell items (either from their store or elements from their tours).
Wow, thanks for the detailed analysis!
I don't know if this can clear things up, but among these objects there was also a Phaser that was presented as a "replica made using original materials and methods". Here it is:
http://marcellorossi.info/PhaserReplica.jpg

I didn't include it in the first place because, contrary to the Globo items which are presented as "screen used", this has a different certificate of authenticity, from Alan Sims, and it clearly says it's a replica.
By the way: does anybody know what this is supposed to be? It was among the other items, but I can't recognize it.
http://marcellorossi.info/MysteriousObject.jpg
