As per question, are there ways to detect photons, and/or to measure their energy, that don't involve any interaction with electrons? And if yes, are there detectors which use photon interactions with other fundamental particles?
Photons are waves of electromagnetic field which interact with charged particles. This means that it is possible to detect photons by observing their interactions with some others charged particles (for example protons, positrons). One possibility of doing this is detecting a change in the trajectory of this particle (looking for Compton scattering which occurs when a photon bounces off the particle). You can watch such a trajectory, for example, in a time projection chamber.
Compared to common techniques of detecting photons (like using a CCD chip), this is very complicated, and I really doubt something like this has been used for light detection. Also, no matter what technique you use, you will end up with an electrical signal which uses electrons.