I think that the idea is to do not live in a seismic zone. You can know that. You want another point of view, is just that.

The frequency content of P-waves and S-waves is not essentially different, so for me the unique clear differentiator remains their respective propagation velocities. You probably need at least two detectors kilometres apart to detect the wave nature from its propagation velocity e.g. by performing correlation between the time data: I doubt you can assess it from a single seismometer, where all waves and propagation paths will have interfered (unless you know you have a single strong seismic source not too far away and a sensor with very low background noise so that you can at a glance separate the successive waves of a single event in the time record: the P-wave is the first one you will detect). If the seismic source is very distant, the P-Wave is diffracted by the boundary layers of the successive layers of the Earth core and these various paths interfere, making the reading far more difficult... Furthermore, if there is a sequence of seismic bursts, the P-waves of the most recent one will be interfering with the S-waves of the earlier ones!

In brief, I do not see any escape from the current signal processing techniques of the world-wide seismic networks, I cannot believe frequency features alone will ever be determining specifically the P-Wave without using a distributed network of sensors to get more knowledge on the source event...

But this is simply stated from my own antecedent knowledge because you ask for external advices, I would not like to discourage your current research!