I think at the apartment before Anakin leaves for Mustafar is the logical place for him to discard it, and therefore the logical place for Obi to obtain it. If someone could film a replica graflex saber against a 'greenscreen' surface and then a robed arm picking it up, Bob could maybe use it to show it on (and being picked up from) a table in the apartment?

Or it doesn't even have to be physically picked up (thus a static image of the prop could be used). Just a lingering shot of it on the table as they discuss Anakin (and then the baby)

I don't remember what the apartment looks like or if such a table exists though.

If I had a full sized replica of the saber, I'd happily do it myself, however I only have the .45 scaled replica.

But that's only if Bob were to decide to go that route. It's my preferred route, but it's not my decision :)