This Duane Eddy number, which had made the UK Singles chart in April 1960, was a big favourite – it was used on stage (and wherever else The Shadows could fit it in, though no BBC Radio take was attempted) probably because it gave a little showcase for each group member. They had taped SHAZAM! live in South Africa in 1961 specifically for overseas customers but it appears that the number was also recorded for the ears of a British audience that year, if not the year before, through the facilities of Radio Luxembourg: it seems to have been featured regularly, perhaps more than any other tune.
There are two different versions surviving, one full, one prematurely faded. The former exists with an introduction by Cliff. He provides the intro: "Now I’d like to call on those kickers, those tons of fun, The Shadows with SHAZAM!", and the number times out at about 1:53. This particular full recording of SHAZAM! seems to have been sandwiched between two other RL tunes, When The Girl In Your Arms and Do You Wanna Dance (the last tune in that show), indicating a broadcast date of around mid-1962 at earliest, though The Shadows' number may have been a repeated item and so recorded some while previously.
Distinguishing features of this complete version are the nicely strutting bassline, the generally punchy approach, and the interjection of bass guitar initially in the first of the two sequences of interjections by all four group members. In the second version, the lead guitar is the first to 'respond', and the performance seems less sprightly. Above all, the tune is faded (as very possibly in the original broadcast) at roughly the one and a quarter minute mark (depending on the tape speed of the example in question!).
Conclusion: the last known RL broadcast date for this number was 9 December 1962. But even though an EMI studio recording was not committed to tape for EMI until August 1963 it looks as if The Shadows recorded SHAZAM! for the R. Luxembourg show at least twice well before that date, perhaps as early as 1960.