I'd be surprised if anything non-traditional happened to them. Even Hitler honored the traditions and let Allied diplomatic staff leave, but put them up first in hotels. (The Swedes were the mechanism from Germany. There was at least one American who got sealifted out as late as the end of '42.)
Thing is, for Japan (from London), they probably had to get to Lisbon. There was no safe route to Japan from western Europe. I think some of the names that show up in the Peace Party in Berlin, The Vatican and Rome were originally stationed in London, so maybe they just made their ways to the continent and filled various functions there.
To my knowledge no one arrested or imprisoned any diplomatic corps members during the war. There was one nasty incident towards the end of the war where the Japanese troops in Manila attacked the Spanish embassy for some reason, doing all sorts of Japanese Occupation Traditional nastiness, but that's the only one I've heard of.