The requirement is for the user to be able to connect stereo headphones to the device and cut off one of the speakers.Your requirement still is not clear to me. Here is a solution for one of the possible interpretations.
The two outputs are identical except for polarity. Both outputs are squarewaves that are referenced to GND, on a fixed DC offset above GND. Normally, driving stereo headphones like this would be a psycho-acoustic problem because the audio in the two speakers would be out of phase. But since you are driving only one speaker at a time, phasing is not an issue.
Alternatively, you can combine the two SPST switches into a single DPDT switch for simple single-toggle action.
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Helmet speakers only tend to be sold with both left and right speakers, but my device should only really be used with one speaker, hence the need to cut one of the speakers off.
Ideally it would be better if you could buy a mono helmet speaker, but these aren't very common. Sometimes the cable length for one speaker is longer than the cable length for the other speaker (as with the Cardo helmet speakers I bought). The picture below are the speakers I have, the short cable has the original 3.5mm jack and was the left speaker. The long cable is the right speaker which I soldered a 3.5mm to but users are unlikely to be able to do this.
So the user should be able to have the option to 1. cut the right speaker cable (at the jack) and use the left speaker which has a short cable or 2. cut the left speaker off (at the jack) and use the right speaker which has a long cable.

The reason for the user using a single speaker is 1. safety, so they have some chance of communicating other people 2. volume, as a single speaker will be louder than driving both speakers (the amp is mono anyway) 3. redundancy, as the other ear usually has another audible device to indicate altitude
Of course, the user could decide to use both speakers, but they do this at their own risk.
Shorting the ring and tip solves this problem, UNLESS a mono jack is inserted which would short the amp output. So it solves the problem for a stereo jack but breaks it for a mono jack.
The DPDT switch in your circuit was what I was hoping to do, but when I looked at DIP switches the current rating is only a few hundred mA which is too low for the amp.
I have very very little space, even a DIP switch will be very difficult to fit. So a DPDT switch with a higher current rating is likely to be too large.
I dont think the capacitors and resistors in your circuit would work, because the output of the amp is not analogue. Its a class D amp, so the output is PWM.
