How to choose speaker impedance for a VERY specific application?
The result depends on exact details and precision of the transducers you must have, i.e. how &quot;medical grade&quot; you want it to be. For example how much you allow for tolerance of acoustic reproduction, is it +/- 1dB or +/- 0.1dB for a given voltage or power signal.
And your parameter about sound pressure is a bit unclear, but assuming you need 100dB SPL at the transducer, not at some other distance like at 1 meter, then I have a solution.
Cheapest possible in-ear headphones can easily reach sensitivity of 100 dB per milliwatt. They are also powered by a standard smartphone audio jack, and fits into nose. Actual impedance may be irrelevant in this application as long as the phone can push enough power into that impedance, and the transducer is sensitive enough to provide you over 100dB SPL with that, but the headphones I have are rated at 16 ohms at 1kHz which is quite typical value. They also can typically take 100mW before getting damage so it will be impossible to break them e.g. by setting smartphone volume to maximum.
Many in-ear headphones also come with multiple sizes of silicone tips for adjusting how tight it fits into the nose - I mean ear.
Downside of this makeshift solution is of course repeatability and calibration, as there is no way to know which volume level is correct for 100dB output, as it depends on the combination of the smartphone and headphones.