Machinbird, that excitation idea is pretty good with a large "if" involved. If the "speaker", the element that imparts the sound in the water, is a resonant element of some sort it should work fine. If not getting energy in through the water to housing discontinuity and then the housing to air discontinuity inside may be difficult. And the resonant element, if there is one, would have to get hard enough to get energy back out.
It might have something as simple as an RC time constant setting the oscillation frequency. With a little more complexity it could be something akin to a watch crystal. (And without driving it so hard it fractures you're not likely to hear it outside of the crystal case.) The next step up might be a tiny higher frequency crystal with a CMOS divider circuit to get it to frequency. I'd vote for the little quartz tuning fork or watch crystal type oscillator.
Stepping backwards a tiny bit if the structure itself plus the transducer has a resonance it might be possible to excite that and notice a distortion in the return signal as you go over the package. The package should have several resonances. Maybe one of them is strong enough to be exploitable.