This might be obliquely enlightening:
"So again, after Lambert convinced Tenzing to join the British, he now had to make sure Tenzing was wearing a Rolex. I asked her why her husband was so pertinent… She explained to me that Raymond was in full believe Rolex, as genevan based, deserved it to be worn on top of a succesful ascent!
In honor of his friendship Tenzing decided to please Lambert, and did not take the “schmutz” she continued!
At first I thought, what’s a “schmutz”, so I asked her…she said her husband always said it like this to her. As we where talking german, the coin dropped and from “schmut”(German for dirty;)I explained her it was Smith, lol! "
https://rolexpassionreport.com/919/t...-norgay-rolex/
Stripping out the obvious pro-Rolex slant (and almost pidgin English), such truth as there might be in that could be construed as: "Tenzing had a Smiths but, being a watch snob, didn't rate it." That lends credence to your argument that it was a Smiths. But this involves crediting the source with some degree of accuracy and integrity (do we really believe him at all? I'm not sure I do.)