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It doesn't make much sense to talk about transmitting "keys" when the encryption is analog.  Since you want to stay away from digital, the encryption and decryption will need to be done in analog hardware.  That has a lot less flexibility than a digital algorithm, so the encryption needs to be more simplistic.

Look at how early "voice scramblers" were done.  That seems to be exactly what you want.

Something analog circuitry can reasonably accomplish is messing with the signal in frequency space.  This is basically what radio transmitters and receivers do.  Your frequency space mangling needs to be a little more complicated than what common radio transmitters do, but not overly so in a world where such things are not widely understood, and there isn't something like today's internet where people who build decryptors can easily have access to others that want to use them.

Maybe the encryption uses three very specific frequencies to transform the voice frequencies with.  Without the specific three frequencies in the receiver, the signal just sounds like gibberish to a human.

Consider how single sideband ham radio transmissions sound unless the receiver is closely tuned to the correct frequency.  Now imagine you have to get three frequencies just right instead of one.  That means you can't simply scan the band until it sounds right.  With three frequencies, two of them would have to be close before scanning the third would yield anything useful.  You'd be searching for a dot in 3-dimensional space, instead of 1-dimensional space like an ordinary radio.

Another technique is synchronous commutation.  You flip polarity, or hetrodyne phase or something at intervals.  The trick is to keep the receiver in sync so that it can do the unflipping at the right times.

Again, lots of stuff like this was done before it was feasible to transmit signals digitally.