@polv Nice find with the self study quiz !
You gave me the idea to try with the Item Inspector and it works too !
The Item Inspector Solution
Using the superb extention: [Userscript] Wanikani Item Inspector
Settings tab: Select Audio in “Enable Features”
Temporary filters
I used my level (1-21) and the item type to “Vocabulary”, obviously creating your own targeted filter is better
Select the filter in the interface
And start the quizz
Then select the “Audio Quizz” and I think it’s exactly what you described 
If you do not already use the item inspector the Self-Study quiz may be easier to setup.