In theory, the noise generated by vertical motion of the stylus in a mono cartridge is cancelled by adding the positive and negative signals from each channel, in a mono cartridge that was created from a stereo cartridge. As I think Fleib is trying to say, since the two channels are never a perfect match, the cancellation effect also can never be absolutely perfect. The same applies to using the mono switch, if your preamplifier has such. I don't own any mono cartridge, but I do use a mono switch when playing mono LPs, and the improvement vs playing mono LPs in stereo is enormous, most notably in the area of reduced noise and an increase in the width of the soundstage. From this I conclude that faux mono cartridges might also work pretty well to generate a mono experience, albeit not perfectly. Anyway, the OP is not asking us to debate this issue. He knows what he wants.
A true mono cartridge, which has only one coil, can have vertical compliance without generating any noise as a result, if there is no mechanism to transduce vertical movement into an audio signal.
Another issue, I much prefer 2-channel mono over the idea of using only one of two speakers when listening to mono. Old habits die hard, I guess. But this is why I personally have no interest in ancient true mono, 2-pin cartridges from the 50s. (While I am a big proponent of vintage stereo cartridges.)