Thank you! You were absolutely right! Very strange that every other cheat doesn't require you to do this.
To select Dan you press and hold start to join the game and keep holding it. The character select screen shows up, you move to your player's random select box and quickly press
either LP, LK, MK, HK, HP, MP (begin at light punch and press all buttons in a counter-clockwise circle)
or HP, HK, MK, LK, LP, MP (begin at heavy punch and press all buttons in a clockwise circle)
This has to be done quite quickly, I found the easiest way to do the cheat consistently do it was to hold start with the "heel" of my right hand. Then I'd use my right hand for all the required punch inputs and for the kicks I would just slide a finger across using my left hand.
Thanks for the idea, it never occurred to me because none of the other cheats required you to hold start so early. For those interested - the "Fight Akuma" cheat works together with the "Play as Dan" cheat. Just keep holding start and immediately after the Dan code you press and hold MP+MK (this is an extremely hard match up!).
I'll post my custom moves list artwork (which includes the cheats) soon. At the moment it's based off the SF ZERO moves list artwork, does anyone have a scan of the SF ALPHA moves list?