Yes, I expect that was a possibility. The Queen also had to make various changes of clothing and jewels. The diamond diadem, worn to the Abbey in the morning, turned up for her to wear on the balcony at the Palace in the evening. There was a jeweler present, I believe, and guards, and evidently someone to transport things. But I wonder whether the ladies also took care of some of the Queen's belongings (like the purse visible in the carriage on the return?) and perhaps assisted with the changes.

Aside from the Queen herself, the maids of honor and the mistress of the robes were really the only women active in the Coronation, and theirs was a role of personal assistance. Whatever form it takes, I doubt if the next Coronation will feature so many elderly white men! I'm sure the Prince of Wales will be surrounded by a more diverse group of people.