You can set up assessments in your Blackboard course that support the submission of an audio file. Note it is the same process for Video files. This is a Blackboard Assignment and can accept multiple files as well and also check for plagiarism utilising Turnitin.
We have guidance for Setting Up a Submission Point, How Students Submit and Self-Paced Course on Creating Better Audio:
How to set up an Assignment: Setting up a Panopto Submission
How to Submit: Creating and Submitting for Assessment
Self-paced course: “Creating Better Audio“
Most students will have either a laptop or a mobile phone to record audio files. If not then students could take out a loan laptop from the IT Centre in the Library which has a bookable loan system.