Has any sqn changed its crest from one approved style to another?
..short answer is yes - 600 (City of London) Sqn - assuming you count the auxies.
Longer answer: The "normal" badge - the "Moon and paperknife" - was approved in 1944. However, since its formation in 1925, 600 had used - unofficially - the arms of the City surmounted by an eagle. A banner bearing this badge was presented to the squadron in 1934 or 35 by Sir Percy Greenaway a former (1932) Lord Mayor. It was presented in memory of Sqn Ldr S B Collett, a CO of the Sqn who was killed at the 1934 Hendon Air Display.
Sqn Ldr Collett was the son of Sir Charles Collett, who was Lord Mayor in 1933. Fast forward to 1951. The Sqn's Honorary Air Commodore, HM Queen Elizabeth (later the Queen Mum) was apprised of the history by the then CO, Sqn Ldr J P Meadows DFC (or Sqn Ldr David Proudlove, depending on your sources), who spoke of the Sqn's reluctance to sever this poignant link with the City. QE speaks to her old man (Geo VI) and very shortly afterwards, Air Ministry Order No N734 of 1951 annouced that the King had "conferred the special privilege upon the Squadron by approving a second badge for its use." As the "City" badge is similar to that on municipal vehicles, it is known as the "dustcart badge".
Here are the two badges:
