A shotgun microphone is a more or less ordinary directional microphone with a slotted "interference tube" in front of it. At low and low-mid frequencies the interference tube has no effect and the microphone is simply a supercardioid (or whatever). Above a certain transition frequency, though, the pattern becomes narrower because of the tube.
The longer the interference tube is, the lower that transition frequency will be, while a shorter interference tube means a higher transition frequency, i.e. for a correspondingly greater portion of the audio range the tube is doing nothing. It's a function of sound wavelengths, which are inversely proportional to sound frequency.
Even with long shotgun microphones--typically ca. 16" or longer--the transition frequency is well up in the midrange. "Short shotguns"--typically 9"-12" long--are as short as possible while still having a meaningful effect on mid-to-upper-midrange frequencies (and higher, of course). If they were any shorter--and no professional shotgun microphone is shorter than that--the narrowing of their pickup pattern would begin only at frequencies so high that it would be relatively useless.
Sorry to say, given the way they work, shotgun microphones fundamentally cannot be miniaturized. In my opinion any manufacturers or dealers who claim otherwise are either ignorant themselves, or are trying to exploit the public's lack of knowledge about how such microphones work.
--best regards