I am always surprised by the subtleties that are embedded in the wave/particle dualism. That is why I read again and again the paragraph in the Dirac's classical text dealing with the single photon interference. Here, it is clearly stated that any measurement of the kick-off of a mirror would cause the photon wave function to collapse, then completely spoiling the quantum interference of the probability distribution. So I wonder if here some ad hoc definiton of measurement is assumed, since in general terms, no matter how I chose to support the mirror, that support will experience a momentum transfer (or radiation pressure) therefore its kick-off will be definitely measured. To be precise, I found no reason to assume that, provided I have a sensitive enough device, I could not measure the single photon radiation pressure (gravitational wave interferometers actually can do that). So the point is that I could, but I don't do it? Subsequent inspections of the Dirac's text unfortunately did not improve my understanding.
I am not sure if I understood the doubt. The problem is about being able to measure the reflected photon? In principle, if the photon is reflected by the mirror it can be detected. However in this case there will be no interference (You know the path of the photon). The wave function between the mirror and the photon become entangled and so the mean value of the one body operator will have no interference