How can I send audio to airport speakers from a stereo system, not a computer?
You have to have a computer in-between.

It probably could be something small like Arduino but it has to be able to communicate with Airport Express in expected way and compress your audio source on the fly to feed to Airport Express as bits and not analog waveform. There is no such device in commercial production as far as I know or if there are they take a great care not to advertise the ability). For example pretty expensive Lynn Network Music players say nothing about Airport Express in their promo materials.

Maybe just maybe every AirPlay compatible receiver can do this but I am not sure since I don't have much experience with them. For this it should be able to get audio from its line in and play it over AirPort Express, maybe doing decoding to the expected format in the process.

Still you might use old computer (you might try old G4 like Mac Mini or iBook might be enough but don't take my word for it test it first), setup audio streaming server on it, get audio from line in and encode it at highest settings it can (preferably lossless in iTunes friendly format since why else?). Then get iTunes to connect to the stream and play it over AE.

Then if you are not using AE with external DAC you should if you care about sound quality since DAC integrated in AE is pretty well crappy one. AE supports Toslink connection.