I'm not sure how nobody within BA as an organisation never became suspicious.
There was never any questioning of his ability to do his job, so I would suggest it went something along the lines of:
1. Simon checks into the hotel as usual with the crew.
2. He's either told his colleagues that he's off to do a bit of charity work and will see them at pick-up or he's just said he's got things to do and will see them at pick-up. Nothing suspicious there and it happens every day. There is certainly no need for everybody to be welded to each other during a layover.
3. Dressed in shorts and t-shirt he makes his way to the orphanage with his bogus captain's uniform in a backpack.
4. Changing before he reaches the establishment, he appears before the welcoming committee as an airline captain, with shiny bars and everything.
5. Does what he does.
6. Reverses the fancy dress costume routine on the way back to the hotel.
7. Appears at pick-up on time and either doesn't discuss his supposed activities with his colleagues (and certainly doesn't discuss his real activities) or he chats about his charity work before the talk moves on to pensions and houses.
An extremely plausible and simple explanation that would lead to no suspicion from anyone. Why is it so difficult to comprehend that BA had no idea of his activities when the guys and girls sitting next to him on the flight deck would have had no idea either?