Have you found a reference which actually confirms C Shore's regiment? I ask, because in his book he is very careful to obscure which unit he is actually commissioned into. Most of the narrative seems to indicate that he is actually in the Army, rather than the RAF - use of Army ranks & terminology, etc. Because he spends most of his service attached to various other units & schools, the RAF references tend to be of third parties.
The main photo of him - on page 135 of the version I have - shows him wearing the uniform & Tam O'shanter of a Scottish battalion. He does include a photo of the "first RAF Regiment sniper course" at Sylt between Dec 45 and Jan 46 - but he is again wearing the same Scottish headgear. I'm not sure the RAF or RAF Regiment have ever worn "regional" uniforms.
Reading his book with a military eye, it looks like he was in the RAF (but not the RAF Regiment; this only formed in 1942, and Shore appears to have been in service since 1939) up to the rank of corporal, then transferred via officer school into an Army unit.