Hi there, Gregory!
What a great question -- one about which I became pretty curious. To that end, I gave a call to the
Bibbidi Bobbidi Boutique at Walt Disney World at (407) WDW-STYLE to ask this very question on your behalf.
The Fairy Godmother at the Boutique suggested that you drop an email to:
wdw.guest.communications@disney.com
Let them know the circumstances you're working with, and ask if it would be possible to arrange a callback or do make the appointment via email. Do this as soon as possible, as this is not an email account that is exclusive to the Boutique and you want to ensure that you make your appointment at your convenience.
The Fairy Godmother to whom I spoke indicated that if the email option doesn't work out, you will have to call
to make those arrangements. However, she provided a tip that might save
you some telephone time.
The earlier in the day you call (Eastern Daylight Time), the less likely you'll have to wait.
The Boutique reservation center opens at 7:00 AM Eastern Daylight Time, or 11:00 AM Greenwich Mean Time, and remains open until 10:00 PM EDT, or 2:00 GMT.
If you start dialing a minute or so before !!:00 AM GMT, your odds of getting a Cast Member's help immediately will definitely increase.
The number - as above - is 1 + (407) WDW-STYLE. Additionally, the information number for Disney's UK Guests is 0800 16 90 730 from the UK; while this number is not meant for reservations, it is possible that the Cast Member can help guide you to another, easier resource.
Please let me know how it goes!
Wishing you a trip full of sparkles!
See you later, celebrator,
-Deborah B.