If the cartridge is aligned as designed by manufacturer, then the cartridge is straight in the headshell. Now move it another tonearm and align it according to that tonearm’s design: it will again be straight in the headshell. To the extent that the tonearms are designed to have different offset angles, those are manifest in the arm tube. So the only thing that could change then is how far in the headshell the cartridge is. But if both tonearms are designed to have the stylus 52mm from the tonearm connection, that doesn’t change either.
If you have difficulty visualizing this, then visualize moving an SPU from one tonearm to another. This is just replicating that with a normal cartridge & headshell.
This makes perfect sense, now that I'm awake, Sampsa55, with (of course) the key element being the offset angle being built into the "bent" portion of the arm wand.
I haven't thought too much about vintage tonearms in the last year, and frankly, I lost track of the 52mm standard, forward offset which is the other key element which allows this to work.
Cheers,
Thom @ Galibier Design