Reason I'm asking: I'm upgrading my sukkah this year to include some AV components including sounds of the desert and music from the time.
I should start out with a link to another thread about the story of Exodus: https://www.reddit.com/r/AskHistorians/comments/22fdp5/is_there_any_reference_to_moses_the_plagues_or/
Even biblical scholars after extensive research have concluded that the story is almost certainly untrue, and there's no evidence that there were even Jews in Egypt at all during any time of antiquity.
That being said, are you interested in Jewish music in the middle east in antiquity, or Egyptian music in antiquity? Either way there won't be a lot, as any surviving written music and instruments it's educated guesswork on how they would have been played.