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I have three Japanese mustang copies, but only one that is playable.

The one that works is a red with yellowed comp stripes that for some reason isn't doing it at all for me. It plays just fine, but I just never feel like picking it up.

One of the others is a white one that looks gorgeous. However the previous owner thought that Yngwie was the coolest dude ever to wear tight pants so he tried some DIY scalloping. He also scraped of the original logo, put in a homemade Fender logo and covered it with what looks like clear nail-polish.

Despite the neck being well fucked up I still pick it up to play way more than the red one. I thought to just swap the necks, but things are never that easy. Despite having at least a few millimeters to spare on each side with the scalloped neck, the neck pocket of the white mustang is too small for the neck of the red one.

What would be the most appropriate way to go from here? Do I file the neck to fit in the pocket, or the pocket to fit the neck? Will filing it potentially mess up the angle of the neck?

Sanding the sides of the neck down would be about 100 x easier to do than enlarging the pocket accurately. Depends on whether the neck is worth a lot more than the body though.
As for the angle - if you mean relative to the body surface, like would affect the action or you would get using a shim, then no. If you mean change the angle so that the strings are off the side of the fretboard, potentially if you really screwed it up, but the screw holes should keep the neck pointing the right way, and if you are careful to sand it flat and parallel with the sides as they are, should be fine.
There is also a bit of angle "play" with Fender necks if they are not too snug in the pocket - you can string them up, back the neck screws off by a quarter turn, and pull the neck up or down before retightening.

I filed the neck for my starblaster, stick some sand paper on a flat surface, and go slowly, it's pretty straight forward.

I tend to work on the 'sand whichever is worth less' principle.