Basically, it's not a cassette. It's a freewheel. On your MTB, the freewheeling mechanism is built into the hub, but on older bikes, it's built into the cogs assembly, which screws onto the hub. You'll need the appropriate freewheel remover, a vice, and perhaps a chainwhip. Replacement freewheels are pretty cheap, and I certainly wouldn't switch out the wheel unless there was another reason. I can't think of any reason why you'd want to change the cranks.
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