Old 6 speed casette on a new modern wheel I've had this old Batavus sprint bike sitting in the shed for years, and recently got into road racing. So I've bought a newish used modern road race bike and recently upgraded it's wheels. Since the old wheels were just lying around I tried fitting them to the good 'ol Batavus. 

They were a little squeeze (research has shown there's a 4mm difference.. 126mm vs 130mm on the newer ones), but I got them in fine. 

Of course, the only problem is is that there's no cassette on the rear wheel I fitted. My question is, can I fit the old cassette on this new wheel? Or will the cassette body be totally different? Or can a cassette body be transferred to the new wheel? I'm not sure how that stuff works.

It's a Shimano 600 6-speed setup.
The old "cassette" is most likely a freewheel. You can see the difference between a cassette and freewheel here

So no, I don't think you will be able to use the old freewheel on the newish wheels (they probably take cassettes). You can just buy a new cassette though (they're cheap), assuming what I said was correct.