From the coronation of Edward VII (1902?) until 1953, military badges, flags, etc. bore a stylised and largely fictitious representation of the Tudor Crown (a crown which does not actually exist, since All Tudor regalia was destroyed after the English Civil War!).
Edward VII, who invented state pomp and pageantry as we know it today, regulated the shape of the Crown in iconography. The new standardised shape was originally called the Tudor crown because it was supposedly modelled on one worn by Henry VII, and it came to be known as the Imperial Crown because its image was standardised throughout the Empire. It has been said that the Tudor Crown's domed shape was chosen to make it more similar to the other European imperial crowns.
In 1952, Sir George Bellew, Garter King of Arms, persuaded the Royal Mint Advisory Committee, and the Committee on the Grant of Honours, Decorations and Medals, that it would be more appropriate if the crown surmounting the Royal Cypher was a realistic representation of the actual Crown of England, rather than being a representation of a crown that did not actually exist. There may also have been some desire to remove the Imperial Crown from iconography to reflect the end of Empire and the start of Commonwealth.
It was subsequently announced that: "The Queen wishes the St Edward's Crown to take the place of the Tudor Crown in all future designs embodying a representation of the crown."
It was decided, however, that existing designs should not be changed unless or until it was necessary to do so, but that when a design embodying the crown had to be changed, the St Edward's Crown should be substituted for the Tudor Crown. It was laid down that no unnecessary expense should be incurred in making the change and where alterations in existing designs would involve such expense they should be deferred. It was stressed that Her Majesty had no objection to two different designs of the crown (i.e. the existing design and the new design) being used concurrently.
Thus current buttons, badges, etc. (though not all squadron badges) have the St Edward's Crown.
But this is simply the actual Crown - and not some 'female' or 'Queen's Crown', and this will be the crown that the next monarch will wear at their coronation, and which will therefore almost certainly be retained.
The idea that there is a "King's Crown" and a different "Queen's Crown" may be 'urban legend' and may be widely reported but it is simply wrong! The design just happened to change with the last change of monarch, which happened to be a change from King to Queen.