It would be a lot less soldering to open the file in Audacity* [freeware] & reverse the phase of one side of the stereo image - https://manual.audacityteam.org/man/invert.html
Sonically, if both sides were phase-inverted you really wouldn't be able to tell. Ears cannot resolve absolute phase, only relative phase.
If one side is out of phase, then sounds which should appear to be in the centre of the stereo field will appear to be 'somewhere outside your head' in a very odd way. Your brain cannot process such sounds, because they would have to be generated from actually inside your head whilst still being heard through your ears rather than by bone conduction, so the brain rejects it as impossible & instead you perceive the sound as being from a very strange kind of 'everywhere'.
*That's a direct download link, just so it doesn't surprise you. It's perfectly safe.