Just to add an additional comment to this thread that may (or may not!) shed some light:
I was following a discussion on Facebook regarding 34346, and a chap posted to say he was very confused by the guitars used by The Shadows in the early years, mainly by the changes in fretboard type (maple to rosewood). He finished the comment with a "throw away" line, saying that he saw them in Cape town Alhambra theatre, 22 march 1961, and "even Cliff had a white Strat for the number "What'd I Say". Of course, I thought of this thread and the picture of the white Strat. Could this be the answer I wonder? I've personally no idea, but the date seems to tie in nicely.
Cliff