Let´s assume you could get speakers which are 100% directional, thus ensuring that nodes would be perfectly located around the room. You would still have to rule out difusion ocurred when the standing waves are formed.
Then, let´s assume all the walls are totally smooth and reflective and provide no difusion at all, but their absortion coefficient is enough for standing waves, and therefore modes, to be formed in the room.
Also we have two ears, and we do not receive the pressure waves in both at the same time or place. Let´s assume for the sake of fun that you cover up one of them and you do the whole path listening with only one ear. Let`s also assume that we only use single tone notes, and do not use the whole spectrum which would mess up our perfect little modes.
Now, Mary had a Little Lamb starts with an E4, which has a fundamental frequency of $329.628 [Hz]$. In a normal room, we can assume sound speed to be around $343 [m/s]$, resulting in a wavelength of about $1.04[m]$ for our E4.
Now, depending on where we place our speaker, we can produce standing waves of one entire wave length, or half a wavelength. But the amplitude with which we will hear the tone, will vary sinusoidally along the standing wave.
If we place each speaker across the wall, but with different distances depending on the tone wavelength (thus standing wave) to be generated, we could mark the spots where you would get zero pressure, and the spots where you would get maximum pressure. Between them, perceived amplitude will vary in a sinusoidal fashion. You could try with little jumps, providing the person walking has good balance and can land on the exact spots marked as antinodes. But then again, you would have to have a speaker for each tone, and if you want to do this for an entire melody in a pathway you would need as much speakers as notes you have in the melody.
So in essence, this cannot be done with no sound anywhere else. It can be done with sinusoidal varying sound between spots, and using a large quantity of speakers.