The size of the hole was smaller in the pre-1960s Zildjians...not sure of the year, but it's on the net somewhere.

You can use vintage stands, and even some modern stands, usually the lighter weight ones, have the smaller post. Even on the modern stands, all you have to do is find a thinner plastic post thing...

Also, the plastic post collar/ring/sleeve/thingy is a "new thing", older stands never had them, that's why you see a lot of keyholing on older cymbals.

Gotta wonder though, do we see more broken cymbals nowadays due to their restricted movement on thicker posts?

Just a thought, that cymbal might have been a set of hand cymbals, hihat OR an older "student" cymbal set. The would account for the small hole on such a small cymbal since it would have been screwed/bolted to wood handles.

Buy yourself a foot or two of surgical rubber tubing - like they use in a medical/chemistry lab.

Cut a length enough to cover the shaft of the tilter, but not the threads. You have to sort of roll it on. Then cut about a half dozen more the same length, and stick 'em in a baggie, and keep that in your stick bag pocket or your trap case as spares, 'cause they don't last but a dozen gigs.

Dig it !

I'm pretty sure that the center hole in cymbals nowadays are 1/8th larger than they used to be back in the 60's (3/8th i think)