Here's a grossly oversimplified schematic of my tig welder, where the Bluetooth-audio hack is drawn in blue.
So it just modulates welding current with music signal.
And here's how it works:
That roundish board was taken from a cheap Bluetooth speaker. I've added a tiny control speaker (behind the round board), just to tell that the audio comes in.
The sound is lacking lows and highs, is a bit distorted, but overall sounds quite good. And quite loud.