I should probably explain the mechanic that can allow your Machamp to re-learn Bullet Punch.
Starting in SwSh, if two Pokémon of the same species (not just evolution family) are in the day-care, one knows an egg move, and the other has an empty move spot, the other also learns the egg move.
So get a Machamp with Bullet Punch and have an open movespot on the shiny. If both are in the day care, the shiny will learn Bullet Punch eventually.
Hope this helps!