I stumbled upon this little $5 device on AliExpress.
https://www.aliexpress.com/item/33057384231.html
It can play 255 different WAV/MP3 based on button input or GPIO-port. It's internal storage is 8 MB, and files can be uploaded by connecting it to a PC via USB.
It might be a simple cheap solution to load software into a ZX81 or Lambda 8300.
I have ordered one, and will give it a try.