“I wonder if aiming a drinking straw at the valve opening and blowing through it would also work.”
It does. I started with various everyday objects. Ballpoint pen barrel was quite ok. The structure above just helps to aim in the middle.
Forgot about the 3D-model: you need to drill the nozzle open to 3-4mm (1/8 – 1/6″). Print has a rough surface that weakens airflow.