Pi filter design for SMPS output ripple
If one was to design at the output a low-pass PI filter with a cutoff
  frequency of 10kHz for example (purely hypothetic), how would one
  proceed?


You would proceed by going backwards and recognizing that you already have capacitance on the output of your current circuit so, all you actually might require is an LC low pass filter to tack on to the output.


  there is no real voltage Vo/Vi transfer function like a LCR filter,
  but instead there are design rules like using the line characteristic
  impedance Z0


That's correct, because you are looking in the wrong place for what you perceive to be the right solution. The right solution is not a Pi filter; it's a low pass filter using L, C and R. Z0 refers to the characteristic impedance of the system i.e. 50 ohms and this type of filter design is for filtering RF signals that require impedance matching. It's not what you want.


  So given all of this, how does one actually implement a PI filter to
  filter the ripple voltage, given your Q factor must be around 0.707 to
  avoid making an oscillator in the process?


Adding a filter to an output does not turn anything into an oscillator. The worst that can happen is that transients from the preceding stage (the power converter) can stimulate ringing voltages on the output and so, that is to be avoided by correct selection of damping resistors.

Use a design like this is my recommendation: -



Picture from this online calculator.

Just make sure that you position the resonant frequency of the filter significantly down below the switching frequency of the converter but not so low that transient changes in the switching converter's output have ringing effects that are too high or unacceptable.