It isn’t clear to me what you’re trying to do. Do you want the users to upload new audio, or just pick an audio file from a list that you will display in the course?
They will never see the Variable Manager (or the Resource Manager). Those are only available to developers in the development environment. You can easily create a drop-down list in Lectora, and that drop-down will set the value of a variable. You can then use the variable to pick which audio file to play. I can provide a sample on request.
There is no built-in way I’m aware of to have the end-user upload a file and play it.