Rather than re-creating a miniature check valve consisting of mircomilimeter sized components, I googled 'valve with no moving parts' and to my surprise found the following:

Source: https://en.wikipedia.org/wiki/Tesla_valve

Nikola Tesla described this device in 1920 allowing fluid to move preferentially in one direction. Although the fluidics have fallen by the way side, I see a useful application of this design in our shunt valve that can be easily manufactured on a 3D printer.