But you probably could do fine, I'd guess, by just
cutting the mains
ground connection for one or the other supply, as appropriate.
No, don;'t do that. FOr one thing most PSUs have a mains filter including
3 delta-connected capacitors. If you take off the ground wire, the
chassis wil try and float at half mains voltage (!). And for another
thing, if you have a component failure, you could end up with mains on
the case or output side, and the fuse won't fail. This will cook whatever
classic device you're powering from it, and may cook you too. Which is
more worrying depends on who you are!
-tony