Yup, car wash products are OK to use.
I was talking to a professional aeroplane cleaner and he told me that these car products are OK.
Don't be tempted to use Fairey liquid as it is corrosive due to its high salt content.
He also recommended Plexus for cleaning the windscreens and I have to agree that the stuff is excellent.
Beware of washing the bird in cold weather if there is a chance of the water freezing into bits such as hinges!
Have fun.
FD