Generally speaking you are correct, but black shoes are worn with service dress in the Royal Irish Regiment.*
As Melchett said - military uniform is anything but!
When I was a young Rockape I did the Infantry Platoon Commanders' Course at Warminster. Back in 1966 there were a lot more regiments than now, and when everyone turned up in service dress for the course photo there were hardly two the same out of around 60 of us! Freezing my whatsits off in a slit trench on Salisbury Plain in February was when the first germ of an idea of applying to go aircrew entered my mind!
*Oops - wrong HRH - you were talking about young Harry. Maybe the same rule applies to the AAC!